ring_theory.noetherian | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

210657c4

(last sync)

refactor(order/well_founded): ditch well_founded_iff_has_min' and well_founded_iff_has_max' (#15071)

The predicate x ≤ y → y = x is no more convenient than ¬ x < y. For this reason, we ditch well_founded.well_founded_iff_has_min' and well_founded.well_founded_iff_has_max' in favor of well_founded.well_founded_iff_has_min (or in some cases, just well_founded.has_min. We also remove the misplaced lemma well_founded.eq_iff_not_lt_of_le, and we golf the theorems that used the removed theorems.

The lemma well_founded.well_founded_iff_has_min has a misleading name when applied on well_founded (>), and mildly screws over dot notation and rewriting by virtue of using >, but a future refactor will fix this.

Diff

@@ -253,20 +253,20 @@ begin
   { intro H,
     constructor,
     intro N,
-    obtain ⟨⟨N₀, h₁⟩, e : N₀ ≤ N, h₂⟩ := well_founded.well_founded_iff_has_max'.mp
+    obtain ⟨⟨N₀, h₁⟩, e : N₀ ≤ N, h₂⟩ := well_founded.has_min
       H { N' : α | N'.1 ≤ N } ⟨⟨⊥, submodule.fg_bot⟩, bot_le⟩,
     convert h₁,
     refine (e.antisymm _).symm,
     by_contra h₃,
     obtain ⟨x, hx₁ : x ∈ N, hx₂ : x ∉ N₀⟩ := set.not_subset.mp h₃,
     apply hx₂,
-    have := h₂ ⟨(R ∙ x) ⊔ N₀, _⟩ _ _,
+    have := eq_of_le_of_not_lt _ (h₂ ⟨(R ∙ x) ⊔ N₀, _⟩ _),
     { injection this with eq,
-      rw ← eq,
+      rw eq,
       exact (le_sup_left : (R ∙ x) ≤ (R ∙ x) ⊔ N₀) (submodule.mem_span_singleton_self _) },
     { exact submodule.fg.sup ⟨{x}, by rw [finset.coe_singleton]⟩ h₁ },
-    { exact sup_le ((submodule.span_singleton_le_iff_mem _ _).mpr hx₁) e },
-    { show N₀ ≤ (R ∙ x) ⊔ N₀, from le_sup_right } }
+    { show N₀ ≤ (R ∙ x) ⊔ N₀, from le_sup_right },
+    { exact sup_le ((submodule.span_singleton_le_iff_mem _ _).mpr hx₁) e } }
 end
 
 variables (R M)
@@ -280,14 +280,12 @@ variables {R M}
 /-- A module is Noetherian iff every nonempty set of submodules has a maximal submodule among them.
 -/
 theorem set_has_maximal_iff_noetherian :
-  (∀ a : set $ submodule R M, a.nonempty → ∃ M' ∈ a, ∀ I ∈ a, M' ≤ I → I = M') ↔
-  is_noetherian R M :=
-by rw [is_noetherian_iff_well_founded, well_founded.well_founded_iff_has_max']
+  (∀ a : set $ submodule R M, a.nonempty → ∃ M' ∈ a, ∀ I ∈ a, ¬ M' < I) ↔ is_noetherian R M :=
+by rw [is_noetherian_iff_well_founded, well_founded.well_founded_iff_has_min]
 
 /-- A module is Noetherian iff every increasing chain of submodules stabilizes. -/
 theorem monotone_stabilizes_iff_noetherian :
-  (∀ (f : ℕ →o submodule R M), ∃ n, ∀ m, n ≤ m → f n = f m)
-    ↔ is_noetherian R M :=
+  (∀ (f : ℕ →o submodule R M), ∃ n, ∀ m, n ≤ m → f n = f m) ↔ is_noetherian R M :=
 by rw [is_noetherian_iff_well_founded, well_founded.monotone_chain_condition]
 
 /-- If `∀ I > J, P I` implies `P J`, then `P` holds for all submodules. -/

da420a8c

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

210657c4

bump to nightly-2024-04-28-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

4a837c64

Diff

@@ -568,13 +568,13 @@ theorem isNoetherian_of_submodule_of_noetherian (R M) [Semiring R] [AddCommMonoi
 #align is_noetherian_of_submodule_of_noetherian isNoetherian_of_submodule_of_noetherian
 -/
 
-#print Submodule.Quotient.isNoetherian /-
-instance Submodule.Quotient.isNoetherian {R} [Ring R] {M} [AddCommGroup M] [Module R M]
-    (N : Submodule R M) [h : IsNoetherian R M] : IsNoetherian R (M ⧸ N) :=
+#print isNoetherian_quotient /-
+instance isNoetherian_quotient {R} [Ring R] {M} [AddCommGroup M] [Module R M] (N : Submodule R M)
+    [h : IsNoetherian R M] : IsNoetherian R (M ⧸ N) :=
   by
   rw [isNoetherian_iff_wellFounded] at h ⊢
   exact OrderEmbedding.wellFounded (Submodule.comapMkQOrderEmbedding N).dual h
-#align submodule.quotient.is_noetherian Submodule.Quotient.isNoetherian
+#align submodule.quotient.is_noetherian isNoetherian_quotient
 -/
 
 #print isNoetherian_of_tower /-

210657c4

bump to nightly-2024-04-25-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

ad7a2212

Diff

@@ -11,7 +11,7 @@ import LinearAlgebra.LinearIndependent
 import Order.CompactlyGenerated.Basic
 import Order.OrderIsoNat
 import RingTheory.Finiteness
-import RingTheory.Nilpotent
+import RingTheory.Nilpotent.Defs
 
 #align_import ring_theory.noetherian from "leanprover-community/mathlib"@"210657c4ea4a4a7b234392f70a3a2a83346dfa90"

210657c4

bump to nightly-2024-04-06-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

e34029c9

Diff

@@ -8,7 +8,7 @@ import Algebra.Algebra.Tower
 import Algebra.Ring.Idempotents
 import GroupTheory.Finiteness
 import LinearAlgebra.LinearIndependent
-import Order.CompactlyGenerated
+import Order.CompactlyGenerated.Basic
 import Order.OrderIsoNat
 import RingTheory.Finiteness
 import RingTheory.Nilpotent

210657c4

bump to nightly-2024-03-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

22f01ce4

Diff

@@ -441,14 +441,14 @@ theorem LinearMap.eventually_disjoint_ker_pow_range_pow [I : IsNoetherian R M] (
     monotone_stabilizes_iff_noetherian.mpr I
       (f.iterate_ker.comp ⟨fun n => n + 1, fun n m w => by linarith⟩)
   specialize w (2 * n + 1) (by linarith only)
-  dsimp at w 
+  dsimp at w
   refine' ⟨n + 1, Nat.succ_ne_zero _, _⟩
   rw [eq_bot_iff]
   rintro - ⟨h, ⟨y, rfl⟩⟩
   rw [mem_bot, ← LinearMap.mem_ker, w]
   erw [LinearMap.mem_ker] at h ⊢
-  change (f ^ (n + 1) * f ^ (n + 1)) y = 0 at h 
-  rw [← pow_add] at h 
+  change (f ^ (n + 1) * f ^ (n + 1)) y = 0 at h
+  rw [← pow_add] at h
   convert h using 3
   ring
 #align is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot LinearMap.eventually_disjoint_ker_pow_range_pow
@@ -461,7 +461,7 @@ theorem IsNoetherian.injective_of_surjective_endomorphism [IsNoetherian R M] (f
   by
   obtain ⟨n, ne, w⟩ := LinearMap.eventually_disjoint_ker_pow_range_pow f
   rw [linear_map.range_eq_top.mpr (LinearMap.iterate_surjective s n), inf_top_eq,
-    LinearMap.ker_eq_bot] at w 
+    LinearMap.ker_eq_bot] at w
   exact LinearMap.injective_of_iterate_injective Ne w
 #align is_noetherian.injective_of_surjective_endomorphism IsNoetherian.injective_of_surjective_endomorphism
 -/
@@ -609,8 +609,8 @@ theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module
       simp only [smul_eq_mul, mul_smul]
       exact finset.smul_sum.symm
   rw [LinearMap.range_eq_top]
-  rintro ⟨n, hn⟩; change n ∈ N at hn 
-  rw [← hs, ← Set.image_id ↑s, Finsupp.mem_span_image_iff_total] at hn 
+  rintro ⟨n, hn⟩; change n ∈ N at hn
+  rw [← hs, ← Set.image_id ↑s, Finsupp.mem_span_image_iff_total] at hn
   rcases hn with ⟨l, hl1, hl2⟩
   refine' ⟨fun x => l x, Subtype.ext _⟩
   change ∑ i in s.attach, l i • (i : M) = n

210657c4

bump to nightly-2023-12-31-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

cfd8a18d

Diff

@@ -392,8 +392,10 @@ universe w
 variable {R M P : Type _} {N : Type w} [Ring R] [AddCommGroup M] [Module R M] [AddCommGroup N]
   [Module R N] [AddCommGroup P] [Module R P]
 
-#print finite_of_linearIndependent /-
-theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M}
+/- warning: finite_of_linear_independent clashes with linear_independent.set_finite_of_is_noetherian -> LinearIndependent.set_finite_of_isNoetherian
+Case conversion may be inaccurate. Consider using '#align finite_of_linear_independent LinearIndependent.set_finite_of_isNoetherianₓ'. -/
+#print LinearIndependent.set_finite_of_isNoetherian /-
+theorem LinearIndependent.set_finite_of_isNoetherian [Nontrivial R] [IsNoetherian R M] {s : Set M}
     (hs : LinearIndependent R (coe : s → M)) : s.Finite :=
   by
   refine'
@@ -411,7 +413,7 @@ theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M
     ⟨⟨fun n => span R (coe ∘ f '' {m | m ≤ n}), fun x y => by
         simp (config := { contextual := true }) [le_antisymm_iff, (this _ _).symm]⟩,
       by dsimp [GT.gt] <;> simp only [lt_iff_le_not_le, (this _ _).symm] <;> tauto⟩
-#align finite_of_linear_independent finite_of_linearIndependent
+#align finite_of_linear_independent LinearIndependent.set_finite_of_isNoetherian
 -/
 
 #print isNoetherian_of_range_eq_ker /-

210657c4

bump to nightly-2023-10-12-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/19c869efa56bbb8b500f2724c0b77261edbfa28c

19581661

Diff

@@ -428,12 +428,12 @@ theorem isNoetherian_of_range_eq_ker [IsNoetherian R M] [IsNoetherian R P] (f :
 #align is_noetherian_of_range_eq_ker isNoetherian_of_range_eq_ker
 -/
 
-#print IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot /-
+#print LinearMap.eventually_disjoint_ker_pow_range_pow /-
 /-- For any endomorphism of a Noetherian module, there is some nontrivial iterate
 with disjoint kernel and range.
 -/
-theorem IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot [I : IsNoetherian R M]
-    (f : M →ₗ[R] M) : ∃ n : ℕ, n ≠ 0 ∧ (f ^ n).ker ⊓ (f ^ n).range = ⊥ :=
+theorem LinearMap.eventually_disjoint_ker_pow_range_pow [I : IsNoetherian R M] (f : M →ₗ[R] M) :
+    ∃ n : ℕ, n ≠ 0 ∧ (f ^ n).ker ⊓ (f ^ n).range = ⊥ :=
   by
   obtain ⟨n, w⟩ :=
     monotone_stabilizes_iff_noetherian.mpr I
@@ -449,7 +449,7 @@ theorem IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot [I : IsNoe
   rw [← pow_add] at h 
   convert h using 3
   ring
-#align is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot
+#align is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot LinearMap.eventually_disjoint_ker_pow_range_pow
 -/
 
 #print IsNoetherian.injective_of_surjective_endomorphism /-
@@ -457,7 +457,7 @@ theorem IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot [I : IsNoe
 theorem IsNoetherian.injective_of_surjective_endomorphism [IsNoetherian R M] (f : M →ₗ[R] M)
     (s : Surjective f) : Injective f :=
   by
-  obtain ⟨n, ne, w⟩ := IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot f
+  obtain ⟨n, ne, w⟩ := LinearMap.eventually_disjoint_ker_pow_range_pow f
   rw [linear_map.range_eq_top.mpr (LinearMap.iterate_surjective s n), inf_top_eq,
     LinearMap.ker_eq_bot] at w 
   exact LinearMap.injective_of_iterate_injective Ne w

210657c4

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,15 +3,15 @@ Copyright (c) 2018 Mario Carneiro, Kevin Buzzard. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Kevin Buzzard
 -/
-import Mathbin.Algebra.Algebra.Subalgebra.Basic
-import Mathbin.Algebra.Algebra.Tower
-import Mathbin.Algebra.Ring.Idempotents
-import Mathbin.GroupTheory.Finiteness
-import Mathbin.LinearAlgebra.LinearIndependent
-import Mathbin.Order.CompactlyGenerated
-import Mathbin.Order.OrderIsoNat
-import Mathbin.RingTheory.Finiteness
-import Mathbin.RingTheory.Nilpotent
+import Algebra.Algebra.Subalgebra.Basic
+import Algebra.Algebra.Tower
+import Algebra.Ring.Idempotents
+import GroupTheory.Finiteness
+import LinearAlgebra.LinearIndependent
+import Order.CompactlyGenerated
+import Order.OrderIsoNat
+import RingTheory.Finiteness
+import RingTheory.Nilpotent
 
 #align_import ring_theory.noetherian from "leanprover-community/mathlib"@"210657c4ea4a4a7b234392f70a3a2a83346dfa90"

210657c4

bump to nightly-2023-08-17-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

60285dcc

Diff

@@ -618,12 +618,12 @@ theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module
 #align is_noetherian_of_fg_of_noetherian isNoetherian_of_fg_of_noetherian
 -/
 
-#print isNoetherian_of_fg_of_noetherian' /-
-theorem isNoetherian_of_fg_of_noetherian' {R M} [Ring R] [AddCommGroup M] [Module R M]
+#print isNoetherian_of_isNoetherianRing_of_finite /-
+theorem isNoetherian_of_isNoetherianRing_of_finite {R M} [Ring R] [AddCommGroup M] [Module R M]
     [IsNoetherianRing R] (h : (⊤ : Submodule R M).FG) : IsNoetherian R M :=
   have : IsNoetherian R (⊤ : Submodule R M) := isNoetherian_of_fg_of_noetherian _ h
   isNoetherian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl)
-#align is_noetherian_of_fg_of_noetherian' isNoetherian_of_fg_of_noetherian'
+#align is_noetherian_of_fg_of_noetherian' isNoetherian_of_isNoetherianRing_of_finite
 -/
 
 #print isNoetherian_span_of_finite /-

210657c4

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2018 Mario Carneiro, Kevin Buzzard. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Kevin Buzzard
-
-! This file was ported from Lean 3 source module ring_theory.noetherian
-! leanprover-community/mathlib commit 210657c4ea4a4a7b234392f70a3a2a83346dfa90
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Algebra.Subalgebra.Basic
 import Mathbin.Algebra.Algebra.Tower
@@ -18,6 +13,8 @@ import Mathbin.Order.OrderIsoNat
 import Mathbin.RingTheory.Finiteness
 import Mathbin.RingTheory.Nilpotent
 
+#align_import ring_theory.noetherian from "leanprover-community/mathlib"@"210657c4ea4a4a7b234392f70a3a2a83346dfa90"
+
 /-!
 # Noetherian rings and modules

210657c4

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -86,13 +86,14 @@ variable [Module R M] [Module R P]
 
 open IsNoetherian
 
-include R
-
+#print isNoetherian_def /-
 /-- An R-module is Noetherian iff all its submodules are finitely-generated. -/
 theorem isNoetherian_def : IsNoetherian R M ↔ ∀ s : Submodule R M, s.FG :=
   ⟨fun h => h.noetherian, IsNoetherian.mk⟩
 #align is_noetherian_def isNoetherian_def
+-/
 
+#print isNoetherian_submodule /-
 theorem isNoetherian_submodule {N : Submodule R M} :
     IsNoetherian R N ↔ ∀ s : Submodule R M, s ≤ N → s.FG :=
   by
@@ -107,16 +108,21 @@ theorem isNoetherian_submodule {N : Submodule R M} :
   have h₃ := ((Submodule.fg_top _).2 h₁).map (↑f : _ →ₗ[R] s)
   exact (Submodule.fg_top _).1 (h₂ ▸ h₃)
 #align is_noetherian_submodule isNoetherian_submodule
+-/
 
+#print isNoetherian_submodule_left /-
 theorem isNoetherian_submodule_left {N : Submodule R M} :
     IsNoetherian R N ↔ ∀ s : Submodule R M, (N ⊓ s).FG :=
   isNoetherian_submodule.trans ⟨fun H s => H _ inf_le_left, fun H s hs => inf_of_le_right hs ▸ H _⟩
 #align is_noetherian_submodule_left isNoetherian_submodule_left
+-/
 
+#print isNoetherian_submodule_right /-
 theorem isNoetherian_submodule_right {N : Submodule R M} :
     IsNoetherian R N ↔ ∀ s : Submodule R M, (s ⊓ N).FG :=
   isNoetherian_submodule.trans ⟨fun H s => H _ inf_le_right, fun H s hs => inf_of_le_left hs ▸ H _⟩
 #align is_noetherian_submodule_right isNoetherian_submodule_right
+-/
 
 #print isNoetherian_submodule' /-
 instance isNoetherian_submodule' [IsNoetherian R M] (N : Submodule R M) : IsNoetherian R N :=
@@ -124,42 +130,54 @@ instance isNoetherian_submodule' [IsNoetherian R M] (N : Submodule R M) : IsNoet
 #align is_noetherian_submodule' isNoetherian_submodule'
 -/
 
+#print isNoetherian_of_le /-
 theorem isNoetherian_of_le {s t : Submodule R M} [ht : IsNoetherian R t] (h : s ≤ t) :
     IsNoetherian R s :=
   isNoetherian_submodule.mpr fun s' hs' => isNoetherian_submodule.mp ht _ (le_trans hs' h)
 #align is_noetherian_of_le isNoetherian_of_le
+-/
 
 variable (M)
 
+#print isNoetherian_of_surjective /-
 theorem isNoetherian_of_surjective (f : M →ₗ[R] P) (hf : f.range = ⊤) [IsNoetherian R M] :
     IsNoetherian R P :=
   ⟨fun s =>
     have : (s.comap f).map f = s := Submodule.map_comap_eq_self <| hf.symm ▸ le_top
     this ▸ (noetherian _).map _⟩
 #align is_noetherian_of_surjective isNoetherian_of_surjective
+-/
 
 variable {M}
 
+#print isNoetherian_of_linearEquiv /-
 theorem isNoetherian_of_linearEquiv (f : M ≃ₗ[R] P) [IsNoetherian R M] : IsNoetherian R P :=
   isNoetherian_of_surjective _ f.toLinearMap f.range
 #align is_noetherian_of_linear_equiv isNoetherian_of_linearEquiv
+-/
 
+#print isNoetherian_top_iff /-
 theorem isNoetherian_top_iff : IsNoetherian R (⊤ : Submodule R M) ↔ IsNoetherian R M :=
   by
   constructor <;> intro h
   · exact isNoetherian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl)
   · exact isNoetherian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl).symm
 #align is_noetherian_top_iff isNoetherian_top_iff
+-/
 
+#print isNoetherian_of_injective /-
 theorem isNoetherian_of_injective [IsNoetherian R P] (f : M →ₗ[R] P) (hf : Function.Injective f) :
     IsNoetherian R M :=
   isNoetherian_of_linearEquiv (LinearEquiv.ofInjective f hf).symm
 #align is_noetherian_of_injective isNoetherian_of_injective
+-/
 
+#print fg_of_injective /-
 theorem fg_of_injective [IsNoetherian R P] {N : Submodule R M} (f : M →ₗ[R] P)
     (hf : Function.Injective f) : N.FG :=
   @IsNoetherian.noetherian _ _ _ (isNoetherian_of_injective f hf) N
 #align fg_of_injective fg_of_injective
+-/
 
 end
 
@@ -180,10 +198,12 @@ instance (priority := 100) IsNoetherian.finite [IsNoetherian R M] : Finite R M :
 
 variable {R M}
 
+#print Module.Finite.of_injective /-
 theorem Finite.of_injective [IsNoetherian R N] (f : M →ₗ[R] N) (hf : Function.Injective f) :
     Finite R M :=
   ⟨fg_of_injective f hf⟩
 #align module.finite.of_injective Module.Finite.of_injective
+-/
 
 end Module
 
@@ -197,18 +217,21 @@ variable [Module R M] [Module R P]
 
 open IsNoetherian
 
-include R
-
+#print isNoetherian_of_ker_bot /-
 theorem isNoetherian_of_ker_bot [IsNoetherian R P] (f : M →ₗ[R] P) (hf : f.ker = ⊥) :
     IsNoetherian R M :=
   isNoetherian_of_linearEquiv (LinearEquiv.ofInjective f <| LinearMap.ker_eq_bot.mp hf).symm
 #align is_noetherian_of_ker_bot isNoetherian_of_ker_bot
+-/
 
+#print fg_of_ker_bot /-
 theorem fg_of_ker_bot [IsNoetherian R P] {N : Submodule R M} (f : M →ₗ[R] P) (hf : f.ker = ⊥) :
     N.FG :=
   @IsNoetherian.noetherian _ _ _ (isNoetherian_of_ker_bot f hf) N
 #align fg_of_ker_bot fg_of_ker_bot
+-/
 
+#print isNoetherian_prod /-
 instance isNoetherian_prod [IsNoetherian R M] [IsNoetherian R P] : IsNoetherian R (M × P) :=
   ⟨fun s =>
     Submodule.fg_of_fg_map_of_fg_inf_ker (LinearMap.snd R M P) (noetherian _) <|
@@ -216,6 +239,7 @@ instance isNoetherian_prod [IsNoetherian R M] [IsNoetherian R P] : IsNoetherian
         fun x ⟨hx1, hx2⟩ => ⟨x.1, Prod.ext rfl <| Eq.symm <| LinearMap.mem_ker.1 hx2⟩
       Submodule.map_comap_eq_self this ▸ (noetherian _).map _⟩
 #align is_noetherian_prod isNoetherian_prod
+-/
 
 #print isNoetherian_pi /-
 instance isNoetherian_pi {R ι : Type _} {M : ι → Type _} [Ring R] [∀ i, AddCommGroup (M i)]
@@ -284,6 +308,7 @@ universe w
 variable {R M P : Type _} {N : Type w} [Semiring R] [AddCommMonoid M] [Module R M] [AddCommMonoid N]
   [Module R N] [AddCommMonoid P] [Module R P]
 
+#print isNoetherian_iff_wellFounded /-
 theorem isNoetherian_iff_wellFounded :
     IsNoetherian R M ↔ WellFounded ((· > ·) : Submodule R M → Submodule R M → Prop) :=
   by
@@ -292,7 +317,9 @@ theorem isNoetherian_iff_wellFounded :
     ⟨fun ⟨h⟩ => fun k => (fg_iff_compact k).mp (h k), fun h =>
       ⟨fun k => (fg_iff_compact k).mpr (h k)⟩⟩
 #align is_noetherian_iff_well_founded isNoetherian_iff_wellFounded
+-/
 
+#print isNoetherian_iff_fg_wellFounded /-
 theorem isNoetherian_iff_fg_wellFounded :
     IsNoetherian R M ↔
       WellFounded
@@ -321,22 +348,27 @@ theorem isNoetherian_iff_fg_wellFounded :
     · show N₀ ≤ (R ∙ x) ⊔ N₀; exact le_sup_right
     · exact sup_le ((Submodule.span_singleton_le_iff_mem _ _).mpr hx₁) e
 #align is_noetherian_iff_fg_well_founded isNoetherian_iff_fg_wellFounded
+-/
 
 variable (R M)
 
+#print wellFounded_submodule_gt /-
 theorem wellFounded_submodule_gt (R M) [Semiring R] [AddCommMonoid M] [Module R M] :
     ∀ [IsNoetherian R M], WellFounded ((· > ·) : Submodule R M → Submodule R M → Prop) :=
   isNoetherian_iff_wellFounded.mp
 #align well_founded_submodule_gt wellFounded_submodule_gt
+-/
 
 variable {R M}
 
+#print set_has_maximal_iff_noetherian /-
 /-- A module is Noetherian iff every nonempty set of submodules has a maximal submodule among them.
 -/
 theorem set_has_maximal_iff_noetherian :
     (∀ a : Set <| Submodule R M, a.Nonempty → ∃ M' ∈ a, ∀ I ∈ a, ¬M' < I) ↔ IsNoetherian R M := by
   rw [isNoetherian_iff_wellFounded, WellFounded.wellFounded_iff_has_min]
 #align set_has_maximal_iff_noetherian set_has_maximal_iff_noetherian
+-/
 
 #print monotone_stabilizes_iff_noetherian /-
 /-- A module is Noetherian iff every increasing chain of submodules stabilizes. -/
@@ -346,11 +378,13 @@ theorem monotone_stabilizes_iff_noetherian :
 #align monotone_stabilizes_iff_noetherian monotone_stabilizes_iff_noetherian
 -/
 
+#print IsNoetherian.induction /-
 /-- If `∀ I > J, P I` implies `P J`, then `P` holds for all submodules. -/
 theorem IsNoetherian.induction [IsNoetherian R M] {P : Submodule R M → Prop}
     (hgt : ∀ I, (∀ J > I, P J) → P I) (I : Submodule R M) : P I :=
   WellFounded.recursion (wellFounded_submodule_gt R M) I hgt
 #align is_noetherian.induction IsNoetherian.induction
+-/
 
 end
 
@@ -361,6 +395,7 @@ universe w
 variable {R M P : Type _} {N : Type w} [Ring R] [AddCommGroup M] [Module R M] [AddCommGroup N]
   [Module R N] [AddCommGroup P] [Module R P]
 
+#print finite_of_linearIndependent /-
 theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M}
     (hs : LinearIndependent R (coe : s → M)) : s.Finite :=
   by
@@ -380,7 +415,9 @@ theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M
         simp (config := { contextual := true }) [le_antisymm_iff, (this _ _).symm]⟩,
       by dsimp [GT.gt] <;> simp only [lt_iff_le_not_le, (this _ _).symm] <;> tauto⟩
 #align finite_of_linear_independent finite_of_linearIndependent
+-/
 
+#print isNoetherian_of_range_eq_ker /-
 /-- If the first and final modules in a short exact sequence are noetherian,
   then the middle module is also noetherian. -/
 theorem isNoetherian_of_range_eq_ker [IsNoetherian R M] [IsNoetherian R P] (f : M →ₗ[R] N)
@@ -392,7 +429,9 @@ theorem isNoetherian_of_range_eq_ker [IsNoetherian R M] [IsNoetherian R P] (f :
       (Submodule.gciMapComap hf) (Submodule.giMapComap hg)
       (by simp [Submodule.map_comap_eq, inf_comm]) (by simp [Submodule.comap_map_eq, h])
 #align is_noetherian_of_range_eq_ker isNoetherian_of_range_eq_ker
+-/
 
+#print IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot /-
 /-- For any endomorphism of a Noetherian module, there is some nontrivial iterate
 with disjoint kernel and range.
 -/
@@ -414,7 +453,9 @@ theorem IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot [I : IsNoe
   convert h using 3
   ring
 #align is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot
+-/
 
+#print IsNoetherian.injective_of_surjective_endomorphism /-
 /-- Any surjective endomorphism of a Noetherian module is injective. -/
 theorem IsNoetherian.injective_of_surjective_endomorphism [IsNoetherian R M] (f : M →ₗ[R] M)
     (s : Surjective f) : Injective f :=
@@ -424,13 +465,17 @@ theorem IsNoetherian.injective_of_surjective_endomorphism [IsNoetherian R M] (f
     LinearMap.ker_eq_bot] at w 
   exact LinearMap.injective_of_iterate_injective Ne w
 #align is_noetherian.injective_of_surjective_endomorphism IsNoetherian.injective_of_surjective_endomorphism
+-/
 
+#print IsNoetherian.bijective_of_surjective_endomorphism /-
 /-- Any surjective endomorphism of a Noetherian module is bijective. -/
 theorem IsNoetherian.bijective_of_surjective_endomorphism [IsNoetherian R M] (f : M →ₗ[R] M)
     (s : Surjective f) : Bijective f :=
   ⟨IsNoetherian.injective_of_surjective_endomorphism f s, s⟩
 #align is_noetherian.bijective_of_surjective_endomorphism IsNoetherian.bijective_of_surjective_endomorphism
+-/
 
+#print IsNoetherian.disjoint_partialSups_eventually_bot /-
 /-- A sequence `f` of submodules of a noetherian module,
 with `f (n+1)` disjoint from the supremum of `f 0`, ..., `f n`,
 is eventually zero.
@@ -452,7 +497,9 @@ theorem IsNoetherian.disjoint_partialSups_eventually_bot [I : IsNoetherian R M]
     ⟨n, fun m p =>
       (h m).eq_bot_of_ge <| sup_eq_left.1 <| (w (m + 1) <| le_add_right p).symm.trans <| w m p⟩
 #align is_noetherian.disjoint_partial_sups_eventually_bot IsNoetherian.disjoint_partialSups_eventually_bot
+-/
 
+#print IsNoetherian.equivPUnitOfProdInjective /-
 /-- If `M ⊕ N` embeds into `M`, for `M` noetherian over `R`, then `N` is trivial.
 -/
 noncomputable def IsNoetherian.equivPUnitOfProdInjective [IsNoetherian R M] (f : M × N →ₗ[R] M)
@@ -467,6 +514,7 @@ noncomputable def IsNoetherian.equivPUnitOfProdInjective [IsNoetherian R M] (f :
   rw [w]
   exact Submodule.botEquivPUnit
 #align is_noetherian.equiv_punit_of_prod_injective IsNoetherian.equivPUnitOfProdInjective
+-/
 
 end
 
@@ -512,12 +560,14 @@ instance (priority := 100) isNoetherian_of_subsingleton (R M) [Subsingleton R] [
 #align is_noetherian_of_subsingleton isNoetherian_of_subsingleton
 -/
 
+#print isNoetherian_of_submodule_of_noetherian /-
 theorem isNoetherian_of_submodule_of_noetherian (R M) [Semiring R] [AddCommMonoid M] [Module R M]
     (N : Submodule R M) (h : IsNoetherian R M) : IsNoetherian R N :=
   by
   rw [isNoetherian_iff_wellFounded] at h ⊢
   exact OrderEmbedding.wellFounded (Submodule.MapSubtype.orderEmbedding N).dual h
 #align is_noetherian_of_submodule_of_noetherian isNoetherian_of_submodule_of_noetherian
+-/
 
 #print Submodule.Quotient.isNoetherian /-
 instance Submodule.Quotient.isNoetherian {R} [Ring R] {M} [AddCommGroup M] [Module R M]
@@ -528,6 +578,7 @@ instance Submodule.Quotient.isNoetherian {R} [Ring R] {M} [AddCommGroup M] [Modu
 #align submodule.quotient.is_noetherian Submodule.Quotient.isNoetherian
 -/
 
+#print isNoetherian_of_tower /-
 /-- If `M / S / R` is a scalar tower, and `M / R` is Noetherian, then `M / S` is
 also noetherian. -/
 theorem isNoetherian_of_tower (R) {S M} [Semiring R] [Semiring S] [AddCommMonoid M] [SMul R S]
@@ -536,7 +587,9 @@ theorem isNoetherian_of_tower (R) {S M} [Semiring R] [Semiring S] [AddCommMonoid
   rw [isNoetherian_iff_wellFounded] at h ⊢
   refine' (Submodule.restrictScalarsEmbedding R S M).dual.WellFounded h
 #align is_noetherian_of_tower isNoetherian_of_tower
+-/
 
+#print isNoetherian_of_fg_of_noetherian /-
 theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module R M]
     (N : Submodule R M) [IsNoetherianRing R] (hN : N.FG) : IsNoetherian R N :=
   by
@@ -566,41 +619,54 @@ theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module
   refine' Finset.sum_subset hl1 fun x _ hx => _
   rw [Finsupp.not_mem_support_iff.1 hx, zero_smul]
 #align is_noetherian_of_fg_of_noetherian isNoetherian_of_fg_of_noetherian
+-/
 
+#print isNoetherian_of_fg_of_noetherian' /-
 theorem isNoetherian_of_fg_of_noetherian' {R M} [Ring R] [AddCommGroup M] [Module R M]
     [IsNoetherianRing R] (h : (⊤ : Submodule R M).FG) : IsNoetherian R M :=
   have : IsNoetherian R (⊤ : Submodule R M) := isNoetherian_of_fg_of_noetherian _ h
   isNoetherian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl)
 #align is_noetherian_of_fg_of_noetherian' isNoetherian_of_fg_of_noetherian'
+-/
 
+#print isNoetherian_span_of_finite /-
 /-- In a module over a noetherian ring, the submodule generated by finitely many vectors is
 noetherian. -/
 theorem isNoetherian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R M]
     [IsNoetherianRing R] {A : Set M} (hA : A.Finite) : IsNoetherian R (Submodule.span R A) :=
   isNoetherian_of_fg_of_noetherian _ (Submodule.fg_def.mpr ⟨A, hA, rfl⟩)
 #align is_noetherian_span_of_finite isNoetherian_span_of_finite
+-/
 
+#print isNoetherianRing_of_surjective /-
 theorem isNoetherianRing_of_surjective (R) [Ring R] (S) [Ring S] (f : R →+* S)
     (hf : Function.Surjective f) [H : IsNoetherianRing R] : IsNoetherianRing S :=
   by
   rw [isNoetherianRing_iff, isNoetherian_iff_wellFounded] at H ⊢
   exact OrderEmbedding.wellFounded (Ideal.orderEmbeddingOfSurjective f hf).dual H
 #align is_noetherian_ring_of_surjective isNoetherianRing_of_surjective
+-/
 
+#print isNoetherianRing_range /-
 instance isNoetherianRing_range {R} [Ring R] {S} [Ring S] (f : R →+* S) [IsNoetherianRing R] :
     IsNoetherianRing f.range :=
   isNoetherianRing_of_surjective R f.range f.range_restrict f.rangeRestrict_surjective
 #align is_noetherian_ring_range isNoetherianRing_range
+-/
 
+#print isNoetherianRing_of_ringEquiv /-
 theorem isNoetherianRing_of_ringEquiv (R) [Ring R] {S} [Ring S] (f : R ≃+* S) [IsNoetherianRing R] :
     IsNoetherianRing S :=
   isNoetherianRing_of_surjective R S f.toRingHom f.toEquiv.Surjective
 #align is_noetherian_ring_of_ring_equiv isNoetherianRing_of_ringEquiv
+-/
 
+#print IsNoetherianRing.isNilpotent_nilradical /-
 theorem IsNoetherianRing.isNilpotent_nilradical (R : Type _) [CommRing R] [IsNoetherianRing R] :
     IsNilpotent (nilradical R) :=
   by
   obtain ⟨n, hn⟩ := Ideal.exists_radical_pow_le_of_fg (⊥ : Ideal R) (IsNoetherian.noetherian _)
   exact ⟨n, eq_bot_iff.mpr hn⟩
 #align is_noetherian_ring.is_nilpotent_nilradical IsNoetherianRing.isNilpotent_nilradical
+-/

210657c4

bump to nightly-2023-06-10-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

3fdc57bc

Diff

@@ -550,10 +550,10 @@ theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module
   · fapply LinearMap.mk
     · exact fun f => ⟨∑ i in s.attach, f i • i.1, N.sum_mem fun c _ => N.smul_mem _ <| this _ c.2⟩
     · intro f g; apply Subtype.eq
-      change (∑ i in s.attach, (f i + g i) • _) = _
+      change ∑ i in s.attach, (f i + g i) • _ = _
       simp only [add_smul, Finset.sum_add_distrib]; rfl
     · intro c f; apply Subtype.eq
-      change (∑ i in s.attach, (c • f i) • _) = _
+      change ∑ i in s.attach, (c • f i) • _ = _
       simp only [smul_eq_mul, mul_smul]
       exact finset.smul_sum.symm
   rw [LinearMap.range_eq_top]
@@ -561,7 +561,7 @@ theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module
   rw [← hs, ← Set.image_id ↑s, Finsupp.mem_span_image_iff_total] at hn 
   rcases hn with ⟨l, hl1, hl2⟩
   refine' ⟨fun x => l x, Subtype.ext _⟩
-  change (∑ i in s.attach, l i • (i : M)) = n
+  change ∑ i in s.attach, l i • (i : M) = n
   rw [@Finset.sum_attach M M s _ fun i => l i • i, ← hl2, Finsupp.total_apply, Finsupp.sum, eq_comm]
   refine' Finset.sum_subset hl1 fun x _ hx => _
   rw [Finsupp.not_mem_support_iff.1 hx, zero_smul]

210657c4

bump to nightly-2023-06-07-05

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

a8c3b45a

Diff

@@ -455,7 +455,7 @@ theorem IsNoetherian.disjoint_partialSups_eventually_bot [I : IsNoetherian R M]
 
 /-- If `M ⊕ N` embeds into `M`, for `M` noetherian over `R`, then `N` is trivial.
 -/
-noncomputable def IsNoetherian.equivPunitOfProdInjective [IsNoetherian R M] (f : M × N →ₗ[R] M)
+noncomputable def IsNoetherian.equivPUnitOfProdInjective [IsNoetherian R M] (f : M × N →ₗ[R] M)
     (i : Injective f) : N ≃ₗ[R] PUnit.{w + 1} :=
   by
   apply Nonempty.some
@@ -466,7 +466,7 @@ noncomputable def IsNoetherian.equivPunitOfProdInjective [IsNoetherian R M] (f :
   refine' (f.tailing_linear_equiv i n).symm ≪≫ₗ _
   rw [w]
   exact Submodule.botEquivPUnit
-#align is_noetherian.equiv_punit_of_prod_injective IsNoetherian.equivPunitOfProdInjective
+#align is_noetherian.equiv_punit_of_prod_injective IsNoetherian.equivPUnitOfProdInjective
 
 end

210657c4

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -307,7 +307,7 @@ theorem isNoetherian_iff_fg_wellFounded :
     constructor
     intro N
     obtain ⟨⟨N₀, h₁⟩, e : N₀ ≤ N, h₂⟩ :=
-      WellFounded.has_min H { N' : α | N'.1 ≤ N } ⟨⟨⊥, Submodule.fg_bot⟩, bot_le⟩
+      WellFounded.has_min H {N' : α | N'.1 ≤ N} ⟨⟨⊥, Submodule.fg_bot⟩, bot_le⟩
     convert h₁
     refine' (e.antisymm _).symm
     by_contra h₃
@@ -368,15 +368,15 @@ theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M
     by_contradiction fun hf =>
       (RelEmbedding.wellFounded_iff_no_descending_seq.1 (wellFounded_submodule_gt R M)).elim' _
   have f : ℕ ↪ s := Set.Infinite.natEmbedding s hf
-  have : ∀ n, coe ∘ f '' { m | m ≤ n } ⊆ s := by rintro n x ⟨y, hy₁, rfl⟩; exact (f y).2
-  have : ∀ a b : ℕ, a ≤ b ↔ span R (coe ∘ f '' { m | m ≤ a }) ≤ span R (coe ∘ f '' { m | m ≤ b }) :=
+  have : ∀ n, coe ∘ f '' {m | m ≤ n} ⊆ s := by rintro n x ⟨y, hy₁, rfl⟩; exact (f y).2
+  have : ∀ a b : ℕ, a ≤ b ↔ span R (coe ∘ f '' {m | m ≤ a}) ≤ span R (coe ∘ f '' {m | m ≤ b}) :=
     by
     intro a b
     rw [span_le_span_iff hs (this a) (this b),
       Set.image_subset_image_iff (subtype.coe_injective.comp f.injective), Set.subset_def]
     exact ⟨fun hab x (hxa : x ≤ a) => le_trans hxa hab, fun hx => hx a (le_refl a)⟩
   exact
-    ⟨⟨fun n => span R (coe ∘ f '' { m | m ≤ n }), fun x y => by
+    ⟨⟨fun n => span R (coe ∘ f '' {m | m ≤ n}), fun x y => by
         simp (config := { contextual := true }) [le_antisymm_iff, (this _ _).symm]⟩,
       by dsimp [GT.gt] <;> simp only [lt_iff_le_not_le, (this _ _).symm] <;> tauto⟩
 #align finite_of_linear_independent finite_of_linearIndependent

210657c4

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -403,14 +403,14 @@ theorem IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot [I : IsNoe
     monotone_stabilizes_iff_noetherian.mpr I
       (f.iterate_ker.comp ⟨fun n => n + 1, fun n m w => by linarith⟩)
   specialize w (2 * n + 1) (by linarith only)
-  dsimp at w
+  dsimp at w 
   refine' ⟨n + 1, Nat.succ_ne_zero _, _⟩
   rw [eq_bot_iff]
   rintro - ⟨h, ⟨y, rfl⟩⟩
   rw [mem_bot, ← LinearMap.mem_ker, w]
-  erw [LinearMap.mem_ker] at h⊢
-  change (f ^ (n + 1) * f ^ (n + 1)) y = 0 at h
-  rw [← pow_add] at h
+  erw [LinearMap.mem_ker] at h ⊢
+  change (f ^ (n + 1) * f ^ (n + 1)) y = 0 at h 
+  rw [← pow_add] at h 
   convert h using 3
   ring
 #align is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot
@@ -421,7 +421,7 @@ theorem IsNoetherian.injective_of_surjective_endomorphism [IsNoetherian R M] (f
   by
   obtain ⟨n, ne, w⟩ := IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot f
   rw [linear_map.range_eq_top.mpr (LinearMap.iterate_surjective s n), inf_top_eq,
-    LinearMap.ker_eq_bot] at w
+    LinearMap.ker_eq_bot] at w 
   exact LinearMap.injective_of_iterate_injective Ne w
 #align is_noetherian.injective_of_surjective_endomorphism IsNoetherian.injective_of_surjective_endomorphism
 
@@ -515,7 +515,7 @@ instance (priority := 100) isNoetherian_of_subsingleton (R M) [Subsingleton R] [
 theorem isNoetherian_of_submodule_of_noetherian (R M) [Semiring R] [AddCommMonoid M] [Module R M]
     (N : Submodule R M) (h : IsNoetherian R M) : IsNoetherian R N :=
   by
-  rw [isNoetherian_iff_wellFounded] at h⊢
+  rw [isNoetherian_iff_wellFounded] at h ⊢
   exact OrderEmbedding.wellFounded (Submodule.MapSubtype.orderEmbedding N).dual h
 #align is_noetherian_of_submodule_of_noetherian isNoetherian_of_submodule_of_noetherian
 
@@ -523,7 +523,7 @@ theorem isNoetherian_of_submodule_of_noetherian (R M) [Semiring R] [AddCommMonoi
 instance Submodule.Quotient.isNoetherian {R} [Ring R] {M} [AddCommGroup M] [Module R M]
     (N : Submodule R M) [h : IsNoetherian R M] : IsNoetherian R (M ⧸ N) :=
   by
-  rw [isNoetherian_iff_wellFounded] at h⊢
+  rw [isNoetherian_iff_wellFounded] at h ⊢
   exact OrderEmbedding.wellFounded (Submodule.comapMkQOrderEmbedding N).dual h
 #align submodule.quotient.is_noetherian Submodule.Quotient.isNoetherian
 -/
@@ -533,7 +533,7 @@ also noetherian. -/
 theorem isNoetherian_of_tower (R) {S M} [Semiring R] [Semiring S] [AddCommMonoid M] [SMul R S]
     [Module S M] [Module R M] [IsScalarTower R S M] (h : IsNoetherian R M) : IsNoetherian S M :=
   by
-  rw [isNoetherian_iff_wellFounded] at h⊢
+  rw [isNoetherian_iff_wellFounded] at h ⊢
   refine' (Submodule.restrictScalarsEmbedding R S M).dual.WellFounded h
 #align is_noetherian_of_tower isNoetherian_of_tower
 
@@ -557,8 +557,8 @@ theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module
       simp only [smul_eq_mul, mul_smul]
       exact finset.smul_sum.symm
   rw [LinearMap.range_eq_top]
-  rintro ⟨n, hn⟩; change n ∈ N at hn
-  rw [← hs, ← Set.image_id ↑s, Finsupp.mem_span_image_iff_total] at hn
+  rintro ⟨n, hn⟩; change n ∈ N at hn 
+  rw [← hs, ← Set.image_id ↑s, Finsupp.mem_span_image_iff_total] at hn 
   rcases hn with ⟨l, hl1, hl2⟩
   refine' ⟨fun x => l x, Subtype.ext _⟩
   change (∑ i in s.attach, l i • (i : M)) = n
@@ -583,7 +583,7 @@ theorem isNoetherian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R
 theorem isNoetherianRing_of_surjective (R) [Ring R] (S) [Ring S] (f : R →+* S)
     (hf : Function.Surjective f) [H : IsNoetherianRing R] : IsNoetherianRing S :=
   by
-  rw [isNoetherianRing_iff, isNoetherian_iff_wellFounded] at H⊢
+  rw [isNoetherianRing_iff, isNoetherian_iff_wellFounded] at H ⊢
   exact OrderEmbedding.wellFounded (Ideal.orderEmbeddingOfSurjective f hf).dual H
 #align is_noetherian_ring_of_surjective isNoetherianRing_of_surjective

210657c4

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -65,7 +65,7 @@ Noetherian, noetherian, Noetherian ring, Noetherian module, noetherian ring, noe
 
 open Set
 
-open BigOperators Pointwise
+open scoped BigOperators Pointwise
 
 #print IsNoetherian /-
 /-- `is_noetherian R M` is the proposition that `M` is a Noetherian `R`-module,

210657c4

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -88,23 +88,11 @@ open IsNoetherian
 
 include R
 
-/- warning: is_noetherian_def -> isNoetherian_def is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_4) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_4 s)
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_4) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_4 s)
-Case conversion may be inaccurate. Consider using '#align is_noetherian_def isNoetherian_defₓ'. -/
 /-- An R-module is Noetherian iff all its submodules are finitely-generated. -/
 theorem isNoetherian_def : IsNoetherian R M ↔ ∀ s : Submodule R M, s.FG :=
   ⟨fun h => h.noetherian, IsNoetherian.mk⟩
 #align is_noetherian_def isNoetherian_def
 
-/- warning: is_noetherian_submodule -> isNoetherian_submodule is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_4))))) s N) -> (Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_4 s))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x N)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_4))))) s N) -> (Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_4 s))
-Case conversion may be inaccurate. Consider using '#align is_noetherian_submodule isNoetherian_submoduleₓ'. -/
 theorem isNoetherian_submodule {N : Submodule R M} :
     IsNoetherian R N ↔ ∀ s : Submodule R M, s ≤ N → s.FG :=
   by
@@ -120,23 +108,11 @@ theorem isNoetherian_submodule {N : Submodule R M} :
   exact (Submodule.fg_top _).1 (h₂ ▸ h₃)
 #align is_noetherian_submodule isNoetherian_submodule
 
-/- warning: is_noetherian_submodule_left -> isNoetherian_submodule_left is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_2 _inst_4) N s))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x N)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.instInfSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) N s))
-Case conversion may be inaccurate. Consider using '#align is_noetherian_submodule_left isNoetherian_submodule_leftₓ'. -/
 theorem isNoetherian_submodule_left {N : Submodule R M} :
     IsNoetherian R N ↔ ∀ s : Submodule R M, (N ⊓ s).FG :=
   isNoetherian_submodule.trans ⟨fun H s => H _ inf_le_left, fun H s hs => inf_of_le_right hs ▸ H _⟩
 #align is_noetherian_submodule_left isNoetherian_submodule_left
 
-/- warning: is_noetherian_submodule_right -> isNoetherian_submodule_right is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_2 _inst_4) s N))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x N)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.instInfSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) s N))
-Case conversion may be inaccurate. Consider using '#align is_noetherian_submodule_right isNoetherian_submodule_rightₓ'. -/
 theorem isNoetherian_submodule_right {N : Submodule R M} :
     IsNoetherian R N ↔ ∀ s : Submodule R M, (s ⊓ N).FG :=
   isNoetherian_submodule.trans ⟨fun H s => H _ inf_le_right, fun H s hs => inf_of_le_left hs ▸ H _⟩
@@ -148,12 +124,6 @@ instance isNoetherian_submodule' [IsNoetherian R M] (N : Submodule R M) : IsNoet
 #align is_noetherian_submodule' isNoetherian_submodule'
 -/
 
-/- warning: is_noetherian_of_le -> isNoetherian_of_le is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4} {t : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4} [ht : IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) t) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 t) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 t)], (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_4))))) s t) -> (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) s) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 s) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 s))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4} {t : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4} [ht : IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x t)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 t) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 t)], (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_4))))) s t) -> (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x s)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 s) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 s))
-Case conversion may be inaccurate. Consider using '#align is_noetherian_of_le isNoetherian_of_leₓ'. -/
 theorem isNoetherian_of_le {s t : Submodule R M} [ht : IsNoetherian R t] (h : s ≤ t) :
     IsNoetherian R s :=
   isNoetherian_submodule.mpr fun s' hs' => isNoetherian_submodule.mp ht _ (le_trans hs' h)
@@ -161,12 +131,6 @@ theorem isNoetherian_of_le {s t : Submodule R M} [ht : IsNoetherian R t] (h : s
 
 variable (M)
 
-/- warning: is_noetherian_of_surjective -> isNoetherian_of_surjective is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} (M : Type.{u2}) {P : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} P] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R P _inst_1 _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Eq.{succ u3} (Submodule.{u1, u3} R P _inst_1 _inst_3 _inst_5) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) f) (Top.top.{u3} (Submodule.{u1, u3} R P _inst_1 _inst_3 _inst_5) (Submodule.hasTop.{u1, u3} R P _inst_1 _inst_3 _inst_5))) -> (forall [_inst_6 : IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_4], IsNoetherian.{u1, u3} R P _inst_1 _inst_3 _inst_5)
-but is expected to have type
-  forall {R : Type.{u3}} (M : Type.{u2}) {P : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} P] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u1} R P _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R P _inst_1 _inst_3 _inst_5) (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) f) (Top.top.{u1} (Submodule.{u3, u1} R P _inst_1 _inst_3 _inst_5) (Submodule.instTopSubmodule.{u3, u1} R P _inst_1 _inst_3 _inst_5))) -> (forall [_inst_6 : IsNoetherian.{u3, u2} R M _inst_1 _inst_2 _inst_4], IsNoetherian.{u3, u1} R P _inst_1 _inst_3 _inst_5)
-Case conversion may be inaccurate. Consider using '#align is_noetherian_of_surjective isNoetherian_of_surjectiveₓ'. -/
 theorem isNoetherian_of_surjective (f : M →ₗ[R] P) (hf : f.range = ⊤) [IsNoetherian R M] :
     IsNoetherian R P :=
   ⟨fun s =>
@@ -176,22 +140,10 @@ theorem isNoetherian_of_surjective (f : M →ₗ[R] P) (hf : f.range = ⊤) [IsN
 
 variable {M}
 
-/- warning: is_noetherian_of_linear_equiv -> isNoetherian_of_linearEquiv is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} P] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R P _inst_1 _inst_3], (LinearEquiv.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M P _inst_2 _inst_3 _inst_4 _inst_5) -> (forall [_inst_6 : IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_4], IsNoetherian.{u1, u3} R P _inst_1 _inst_3 _inst_5)
-but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u2}} {P : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} P] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u1} R P _inst_1 _inst_3], (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M P _inst_2 _inst_3 _inst_4 _inst_5) -> (forall [_inst_6 : IsNoetherian.{u3, u2} R M _inst_1 _inst_2 _inst_4], IsNoetherian.{u3, u1} R P _inst_1 _inst_3 _inst_5)
-Case conversion may be inaccurate. Consider using '#align is_noetherian_of_linear_equiv isNoetherian_of_linearEquivₓ'. -/
 theorem isNoetherian_of_linearEquiv (f : M ≃ₗ[R] P) [IsNoetherian R M] : IsNoetherian R P :=
   isNoetherian_of_surjective _ f.toLinearMap f.range
 #align is_noetherian_of_linear_equiv isNoetherian_of_linearEquiv
 
-/- warning: is_noetherian_top_iff -> isNoetherian_top_iff is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.hasTop.{u1, u2} R M _inst_1 _inst_2 _inst_4))) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.hasTop.{u1, u2} R M _inst_1 _inst_2 _inst_4))) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.hasTop.{u1, u2} R M _inst_1 _inst_2 _inst_4)))) (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_4)
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x (Top.top.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_4)))) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 (Top.top.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_4))) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 (Top.top.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_4)))) (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_4)
-Case conversion may be inaccurate. Consider using '#align is_noetherian_top_iff isNoetherian_top_iffₓ'. -/
 theorem isNoetherian_top_iff : IsNoetherian R (⊤ : Submodule R M) ↔ IsNoetherian R M :=
   by
   constructor <;> intro h
@@ -199,23 +151,11 @@ theorem isNoetherian_top_iff : IsNoetherian R (⊤ : Submodule R M) ↔ IsNoethe
   · exact isNoetherian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl).symm
 #align is_noetherian_top_iff isNoetherian_top_iff
 
-/- warning: is_noetherian_of_injective -> isNoetherian_of_injective is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} P] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u1, u3} R P _inst_1 _inst_3 _inst_5] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u2, succ u3} M P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_4)
-but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} P] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R P _inst_1 _inst_3 _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M P (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (IsNoetherian.{u3, u1} R M _inst_1 _inst_2 _inst_4)
-Case conversion may be inaccurate. Consider using '#align is_noetherian_of_injective isNoetherian_of_injectiveₓ'. -/
 theorem isNoetherian_of_injective [IsNoetherian R P] (f : M →ₗ[R] P) (hf : Function.Injective f) :
     IsNoetherian R M :=
   isNoetherian_of_linearEquiv (LinearEquiv.ofInjective f hf).symm
 #align is_noetherian_of_injective isNoetherian_of_injective
 
-/- warning: fg_of_injective -> fg_of_injective is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} P] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u1, u3} R P _inst_1 _inst_3 _inst_5] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4} (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u2, succ u3} M P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)
-but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} P] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R P _inst_1 _inst_3 _inst_5] {N : Submodule.{u3, u1} R M _inst_1 _inst_2 _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M P (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (Submodule.FG.{u3, u1} R M _inst_1 _inst_2 _inst_4 N)
-Case conversion may be inaccurate. Consider using '#align fg_of_injective fg_of_injectiveₓ'. -/
 theorem fg_of_injective [IsNoetherian R P] {N : Submodule R M} (f : M →ₗ[R] P)
     (hf : Function.Injective f) : N.FG :=
   @IsNoetherian.noetherian _ _ _ (isNoetherian_of_injective f hf) N
@@ -240,12 +180,6 @@ instance (priority := 100) IsNoetherian.finite [IsNoetherian R M] : Finite R M :
 
 variable {R M}
 
-/- warning: module.finite.of_injective -> Module.Finite.of_injective is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u1, u3} R N _inst_1 _inst_3 _inst_5] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u2, succ u3} M N (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M N _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (Module.Finite.{u1, u2} R M _inst_1 _inst_2 _inst_4)
-but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} N] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R N _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R N _inst_1 _inst_3 _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M N _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (Module.Finite.{u3, u1} R M _inst_1 _inst_2 _inst_4)
-Case conversion may be inaccurate. Consider using '#align module.finite.of_injective Module.Finite.of_injectiveₓ'. -/
 theorem Finite.of_injective [IsNoetherian R N] (f : M →ₗ[R] N) (hf : Function.Injective f) :
     Finite R M :=
   ⟨fg_of_injective f hf⟩
@@ -265,34 +199,16 @@ open IsNoetherian
 
 include R
 
-/- warning: is_noetherian_of_ker_bot -> isNoetherian_of_ker_bot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_6 : IsNoetherian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5), (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) -> (IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)
-but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : Module.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_6 : IsNoetherian.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.ker.{u3, u3, u1, u2, max u1 u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u1, u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f) (Bot.bot.{u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instBotSubmodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) -> (IsNoetherian.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)
-Case conversion may be inaccurate. Consider using '#align is_noetherian_of_ker_bot isNoetherian_of_ker_botₓ'. -/
 theorem isNoetherian_of_ker_bot [IsNoetherian R P] (f : M →ₗ[R] P) (hf : f.ker = ⊥) :
     IsNoetherian R M :=
   isNoetherian_of_linearEquiv (LinearEquiv.ofInjective f <| LinearMap.ker_eq_bot.mp hf).symm
 #align is_noetherian_of_ker_bot isNoetherian_of_ker_bot
 
-/- warning: fg_of_ker_bot -> fg_of_ker_bot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_6 : IsNoetherian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5] {N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4} (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5), (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) -> (Submodule.FG.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N)
-but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : Module.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_6 : IsNoetherian.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_5] {N : Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.ker.{u3, u3, u1, u2, max u1 u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u1, u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f) (Bot.bot.{u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instBotSubmodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) -> (Submodule.FG.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 N)
-Case conversion may be inaccurate. Consider using '#align fg_of_ker_bot fg_of_ker_botₓ'. -/
 theorem fg_of_ker_bot [IsNoetherian R P] {N : Submodule R M} (f : M →ₗ[R] P) (hf : f.ker = ⊥) :
     N.FG :=
   @IsNoetherian.noetherian _ _ _ (isNoetherian_of_ker_bot f hf) N
 #align fg_of_ker_bot fg_of_ker_bot
 
-/- warning: is_noetherian_prod -> isNoetherian_prod is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_6 : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4] [_inst_7 : IsNoetherian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5], IsNoetherian.{u1, max u2 u3} R (Prod.{u2, u3} M P) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)) (Prod.module.{u1, u2, u3} R M P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_6 : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4] [_inst_7 : IsNoetherian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5], IsNoetherian.{u1, max u3 u2} R (Prod.{u2, u3} M P) (Ring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)) (Prod.module.{u1, u2, u3} R M P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5)
-Case conversion may be inaccurate. Consider using '#align is_noetherian_prod isNoetherian_prodₓ'. -/
 instance isNoetherian_prod [IsNoetherian R M] [IsNoetherian R P] : IsNoetherian R (M × P) :=
   ⟨fun s =>
     Submodule.fg_of_fg_map_of_fg_inf_ker (LinearMap.snd R M P) (noetherian _) <|
@@ -368,12 +284,6 @@ universe w
 variable {R M P : Type _} {N : Type w} [Semiring R] [AddCommMonoid M] [Module R M] [AddCommMonoid N]
   [Module R N] [AddCommMonoid P] [Module R P]
 
-/- warning: is_noetherian_iff_well_founded -> isNoetherian_iff_wellFounded is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (GT.gt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))))))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2236 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.RingTheory.Noetherian._hyg.2238 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => GT.gt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.RingTheory.Noetherian._hyg.2236 x._@.Mathlib.RingTheory.Noetherian._hyg.2238))
-Case conversion may be inaccurate. Consider using '#align is_noetherian_iff_well_founded isNoetherian_iff_wellFoundedₓ'. -/
 theorem isNoetherian_iff_wellFounded :
     IsNoetherian R M ↔ WellFounded ((· > ·) : Submodule R M → Submodule R M → Prop) :=
   by
@@ -383,12 +293,6 @@ theorem isNoetherian_iff_wellFounded :
       ⟨fun k => (fg_iff_compact k).mpr (h k)⟩⟩
 #align is_noetherian_iff_well_founded isNoetherian_iff_wellFounded
 
-/- warning: is_noetherian_iff_fg_well_founded -> isNoetherian_iff_fg_wellFounded is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_3 N)) (GT.gt.{u2} (Subtype.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_3 N)) (Subtype.hasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_3 N))))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u1} (Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2445 : Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (x._@.Mathlib.RingTheory.Noetherian._hyg.2447 : Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) => GT.gt.{u1} (Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (Subtype.lt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) x._@.Mathlib.RingTheory.Noetherian._hyg.2445 x._@.Mathlib.RingTheory.Noetherian._hyg.2447))
-Case conversion may be inaccurate. Consider using '#align is_noetherian_iff_fg_well_founded isNoetherian_iff_fg_wellFoundedₓ'. -/
 theorem isNoetherian_iff_fg_wellFounded :
     IsNoetherian R M ↔
       WellFounded
@@ -420,12 +324,6 @@ theorem isNoetherian_iff_fg_wellFounded :
 
 variable (R M)
 
-/- warning: well_founded_submodule_gt -> wellFounded_submodule_gt is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_8 : Semiring.{u1} R] [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} R M _inst_8 _inst_9] [_inst_11 : IsNoetherian.{u1, u2} R M _inst_8 _inst_9 _inst_10], WellFounded.{succ u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (GT.gt.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (Submodule.completeLattice.{u1, u2} R M _inst_8 _inst_9 _inst_10))))))
-but is expected to have type
-  forall (R : Type.{u2}) (M : Type.{u1}) [_inst_8 : Semiring.{u2} R] [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} R M _inst_8 _inst_9] [_inst_11 : IsNoetherian.{u2, u1} R M _inst_8 _inst_9 _inst_10], WellFounded.{succ u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2840 : Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (x._@.Mathlib.RingTheory.Noetherian._hyg.2842 : Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) => GT.gt.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (Submodule.completeLattice.{u2, u1} R M _inst_8 _inst_9 _inst_10))))) x._@.Mathlib.RingTheory.Noetherian._hyg.2840 x._@.Mathlib.RingTheory.Noetherian._hyg.2842)
-Case conversion may be inaccurate. Consider using '#align well_founded_submodule_gt wellFounded_submodule_gtₓ'. -/
 theorem wellFounded_submodule_gt (R M) [Semiring R] [AddCommMonoid M] [Module R M] :
     ∀ [IsNoetherian R M], WellFounded ((· > ·) : Submodule R M → Submodule R M → Prop) :=
   isNoetherian_iff_wellFounded.mp
@@ -433,12 +331,6 @@ theorem wellFounded_submodule_gt (R M) [Semiring R] [AddCommMonoid M] [Module R
 
 variable {R M}
 
-/- warning: set_has_maximal_iff_noetherian -> set_has_maximal_iff_noetherian is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (forall (a : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) a) -> (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (M' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{0} (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) => forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) I a) -> (Not (LT.lt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) M' I)))))) (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (forall (a : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) a) -> (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (M' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => And (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) (forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) I a) -> (Not (LT.lt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) M' I)))))) (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3)
-Case conversion may be inaccurate. Consider using '#align set_has_maximal_iff_noetherian set_has_maximal_iff_noetherianₓ'. -/
 /-- A module is Noetherian iff every nonempty set of submodules has a maximal submodule among them.
 -/
 theorem set_has_maximal_iff_noetherian :
@@ -454,12 +346,6 @@ theorem monotone_stabilizes_iff_noetherian :
 #align monotone_stabilizes_iff_noetherian monotone_stabilizes_iff_noetherian
 -/
 
-/- warning: is_noetherian.induction -> IsNoetherian.induction is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_8 : IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3] {P : (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) -> Prop}, (forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (forall (J : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (GT.gt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) J I) -> (P J)) -> (P I)) -> (forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), P I)
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] [_inst_8 : IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3] {P : (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) -> Prop}, (forall (I : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), (forall (J : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), (GT.gt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) J I) -> (P J)) -> (P I)) -> (forall (I : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), P I)
-Case conversion may be inaccurate. Consider using '#align is_noetherian.induction IsNoetherian.inductionₓ'. -/
 /-- If `∀ I > J, P I` implies `P J`, then `P` holds for all submodules. -/
 theorem IsNoetherian.induction [IsNoetherian R M] {P : Submodule R M → Prop}
     (hgt : ∀ I, (∀ J > I, P J) → P I) (I : Submodule R M) : P I :=
@@ -475,12 +361,6 @@ universe w
 variable {R M P : Type _} {N : Type w} [Ring R] [AddCommGroup M] [Module R M] [AddCommGroup N]
   [Module R N] [AddCommGroup P] [Module R P]
 
-/- warning: finite_of_linear_independent -> finite_of_linearIndependent is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Nontrivial.{u1} R] [_inst_9 : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] {s : Set.{u2} M}, (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s)))))) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> (Set.Finite.{u2} M s)
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R] [_inst_9 : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] {s : Set.{u1} M}, (LinearIndependent.{u1, u2, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x s)) R M (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x s)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) -> (Set.Finite.{u1} M s)
-Case conversion may be inaccurate. Consider using '#align finite_of_linear_independent finite_of_linearIndependentₓ'. -/
 theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M}
     (hs : LinearIndependent R (coe : s → M)) : s.Finite :=
   by
@@ -501,9 +381,6 @@ theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M
       by dsimp [GT.gt] <;> simp only [lt_iff_le_not_le, (this _ _).symm] <;> tauto⟩
 #align finite_of_linear_independent finite_of_linearIndependent
 
-/- warning: is_noetherian_of_range_eq_ker -> isNoetherian_of_range_eq_ker is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_noetherian_of_range_eq_ker isNoetherian_of_range_eq_kerₓ'. -/
 /-- If the first and final modules in a short exact sequence are noetherian,
   then the middle module is also noetherian. -/
 theorem isNoetherian_of_range_eq_ker [IsNoetherian R M] [IsNoetherian R P] (f : M →ₗ[R] N)
@@ -516,9 +393,6 @@ theorem isNoetherian_of_range_eq_ker [IsNoetherian R M] [IsNoetherian R P] (f :
       (by simp [Submodule.map_comap_eq, inf_comm]) (by simp [Submodule.comap_map_eq, h])
 #align is_noetherian_of_range_eq_ker isNoetherian_of_range_eq_ker
 
-/- warning: is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot -> IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_botₓ'. -/
 /-- For any endomorphism of a Noetherian module, there is some nontrivial iterate
 with disjoint kernel and range.
 -/
@@ -541,12 +415,6 @@ theorem IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot [I : IsNoe
   ring
 #align is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot
 
-/- warning: is_noetherian.injective_of_surjective_endomorphism -> IsNoetherian.injective_of_surjective_endomorphism is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Injective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Injective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
-Case conversion may be inaccurate. Consider using '#align is_noetherian.injective_of_surjective_endomorphism IsNoetherian.injective_of_surjective_endomorphismₓ'. -/
 /-- Any surjective endomorphism of a Noetherian module is injective. -/
 theorem IsNoetherian.injective_of_surjective_endomorphism [IsNoetherian R M] (f : M →ₗ[R] M)
     (s : Surjective f) : Injective f :=
@@ -557,24 +425,12 @@ theorem IsNoetherian.injective_of_surjective_endomorphism [IsNoetherian R M] (f
   exact LinearMap.injective_of_iterate_injective Ne w
 #align is_noetherian.injective_of_surjective_endomorphism IsNoetherian.injective_of_surjective_endomorphism
 
-/- warning: is_noetherian.bijective_of_surjective_endomorphism -> IsNoetherian.bijective_of_surjective_endomorphism is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Bijective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Bijective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
-Case conversion may be inaccurate. Consider using '#align is_noetherian.bijective_of_surjective_endomorphism IsNoetherian.bijective_of_surjective_endomorphismₓ'. -/
 /-- Any surjective endomorphism of a Noetherian module is bijective. -/
 theorem IsNoetherian.bijective_of_surjective_endomorphism [IsNoetherian R M] (f : M →ₗ[R] M)
     (s : Surjective f) : Bijective f :=
   ⟨IsNoetherian.injective_of_surjective_endomorphism f s, s⟩
 #align is_noetherian.bijective_of_surjective_endomorphism IsNoetherian.bijective_of_surjective_endomorphism
 
-/- warning: is_noetherian.disjoint_partial_sups_eventually_bot -> IsNoetherian.disjoint_partialSups_eventually_bot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [I : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : Nat -> (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)), (forall (n : Nat), Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) (Submodule.orderBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{succ u2, succ u2} (OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))))) (fun (_x : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))))) => Nat -> (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (OrderHom.hasCoeToFun.{0, u2} Nat (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))))) (partialSups.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) f) n) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) -> (Exists.{1} Nat (fun (n : Nat) => forall (m : Nat), (LE.le.{0} Nat Nat.hasLe n m) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f m) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [I : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : Nat -> (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)), (forall (n : Nat), Disjoint.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OrderHom.toFun.{0, u1} Nat (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SemilatticeSup.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) (partialSups.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) f) n) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) -> (Exists.{1} Nat (fun (n : Nat) => forall (m : Nat), (LE.le.{0} Nat instLENat n m) -> (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f m) (Bot.bot.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))
-Case conversion may be inaccurate. Consider using '#align is_noetherian.disjoint_partial_sups_eventually_bot IsNoetherian.disjoint_partialSups_eventually_botₓ'. -/
 /-- A sequence `f` of submodules of a noetherian module,
 with `f (n+1)` disjoint from the supremum of `f 0`, ..., `f n`,
 is eventually zero.
@@ -597,12 +453,6 @@ theorem IsNoetherian.disjoint_partialSups_eventually_bot [I : IsNoetherian R M]
       (h m).eq_bot_of_ge <| sup_eq_left.1 <| (w (m + 1) <| le_add_right p).symm.trans <| w m p⟩
 #align is_noetherian.disjoint_partial_sups_eventually_bot IsNoetherian.disjoint_partialSups_eventually_bot
 
-/- warning: is_noetherian.equiv_punit_of_prod_injective -> IsNoetherian.equivPunitOfProdInjective is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_8 : IsNoetherian.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, max u3 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3), (Function.Injective.{max (succ u3) (succ u1), succ u3} (Prod.{u3, u1} M N) M (coeFn.{max (succ (max u3 u1)) (succ u3), max (succ (max u3 u1)) (succ u3)} (LinearMap.{u2, u2, max u3 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3) (fun (_x : LinearMap.{u2, u2, max u3 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3) => (Prod.{u3, u1} M N) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u3 u1, u3} R R (Prod.{u3, u1} M N) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (IsNoetherian.equivPunitOfProdInjective._proof_1.{u2} R _inst_1) (IsNoetherian.equivPunitOfProdInjective._proof_2.{u2} R _inst_1) N PUnit.{succ u1} (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} PUnit.{succ u1} PUnit.addCommGroup.{u1}) _inst_5 (PUnit.module.{u2, u1} R (Ring.toSemiring.{u2} R _inst_1)))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_8 : IsNoetherian.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, max u1 u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3), (Function.Injective.{max (succ u1) (succ u3), succ u3} (Prod.{u3, u1} M N) M (FunLike.coe.{max (succ u1) (succ u3), max (succ u1) (succ u3), succ u3} (LinearMap.{u2, u2, max u1 u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3) (Prod.{u3, u1} M N) (fun (_x : Prod.{u3, u1} M N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Prod.{u3, u1} M N) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u3, u3} R R (Prod.{u3, u1} M N) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) N PUnit.{succ u1} (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} PUnit.{succ u1} (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} PUnit.{succ u1} PUnit.linearOrderedCancelAddCommMonoid.{u1})) _inst_5 (PUnit.module.{u2, u1} R (Ring.toSemiring.{u2} R _inst_1)))
-Case conversion may be inaccurate. Consider using '#align is_noetherian.equiv_punit_of_prod_injective IsNoetherian.equivPunitOfProdInjectiveₓ'. -/
 /-- If `M ⊕ N` embeds into `M`, for `M` noetherian over `R`, then `N` is trivial.
 -/
 noncomputable def IsNoetherian.equivPunitOfProdInjective [IsNoetherian R M] (f : M × N →ₗ[R] M)
@@ -662,12 +512,6 @@ instance (priority := 100) isNoetherian_of_subsingleton (R M) [Subsingleton R] [
 #align is_noetherian_of_subsingleton isNoetherian_of_subsingleton
 -/
 
-/- warning: is_noetherian_of_submodule_of_noetherian -> isNoetherian_of_submodule_of_noetherian is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3) -> (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 N))
-but is expected to have type
-  forall (R : Type.{u2}) (M : Type.{u1}) [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3) -> (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x N)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 N) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 N))
-Case conversion may be inaccurate. Consider using '#align is_noetherian_of_submodule_of_noetherian isNoetherian_of_submodule_of_noetherianₓ'. -/
 theorem isNoetherian_of_submodule_of_noetherian (R M) [Semiring R] [AddCommMonoid M] [Module R M]
     (N : Submodule R M) (h : IsNoetherian R M) : IsNoetherian R N :=
   by
@@ -684,12 +528,6 @@ instance Submodule.Quotient.isNoetherian {R} [Ring R] {M} [AddCommGroup M] [Modu
 #align submodule.quotient.is_noetherian Submodule.Quotient.isNoetherian
 -/
 
-/- warning: is_noetherian_of_tower -> isNoetherian_of_tower is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) {S : Type.{u2}} {M : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : SMul.{u1, u2} R S] [_inst_5 : Module.{u2, u3} S M _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R M _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S M _inst_4 (SMulZeroClass.toHasSmul.{u2, u3} S M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S M (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S M (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Module.toMulActionWithZero.{u2, u3} S M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Module.toMulActionWithZero.{u1, u3} R M _inst_1 _inst_3 _inst_6))))], (IsNoetherian.{u1, u3} R M _inst_1 _inst_3 _inst_6) -> (IsNoetherian.{u2, u3} S M _inst_2 _inst_3 _inst_5)
-but is expected to have type
-  forall (R : Type.{u3}) {S : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : SMul.{u3, u2} R S] [_inst_5 : Module.{u2, u1} S M _inst_2 _inst_3] [_inst_6 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u3, u2, u1} R S M _inst_4 (SMulZeroClass.toSMul.{u2, u1} S M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} S M (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} S M (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} S M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u3, u1} R M _inst_1 _inst_3 _inst_6))))], (IsNoetherian.{u3, u1} R M _inst_1 _inst_3 _inst_6) -> (IsNoetherian.{u2, u1} S M _inst_2 _inst_3 _inst_5)
-Case conversion may be inaccurate. Consider using '#align is_noetherian_of_tower isNoetherian_of_towerₓ'. -/
 /-- If `M / S / R` is a scalar tower, and `M / R` is Noetherian, then `M / S` is
 also noetherian. -/
 theorem isNoetherian_of_tower (R) {S M} [Semiring R] [Semiring S] [AddCommMonoid M] [SMul R S]
@@ -699,12 +537,6 @@ theorem isNoetherian_of_tower (R) {S M} [Semiring R] [Semiring S] [AddCommMonoid
   refine' (Submodule.restrictScalarsEmbedding R S M).dual.WellFounded h
 #align is_noetherian_of_tower isNoetherian_of_tower
 
-/- warning: is_noetherian_of_fg_of_noetherian -> isNoetherian_of_fg_of_noetherian is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_4 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], (Submodule.FG.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 N) -> (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) N) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 N) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 N))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (N : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) [_inst_4 : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], (Submodule.FG.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 N) -> (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x N)) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 N) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 N))
-Case conversion may be inaccurate. Consider using '#align is_noetherian_of_fg_of_noetherian isNoetherian_of_fg_of_noetherianₓ'. -/
 theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module R M]
     (N : Submodule R M) [IsNoetherianRing R] (hN : N.FG) : IsNoetherian R N :=
   by
@@ -735,24 +567,12 @@ theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module
   rw [Finsupp.not_mem_support_iff.1 hx, zero_smul]
 #align is_noetherian_of_fg_of_noetherian isNoetherian_of_fg_of_noetherian
 
-/- warning: is_noetherian_of_fg_of_noetherian' -> isNoetherian_of_fg_of_noetherian' is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], (Submodule.FG.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) -> (IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], (Submodule.FG.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) -> (IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)
-Case conversion may be inaccurate. Consider using '#align is_noetherian_of_fg_of_noetherian' isNoetherian_of_fg_of_noetherian'ₓ'. -/
 theorem isNoetherian_of_fg_of_noetherian' {R M} [Ring R] [AddCommGroup M] [Module R M]
     [IsNoetherianRing R] (h : (⊤ : Submodule R M).FG) : IsNoetherian R M :=
   have : IsNoetherian R (⊤ : Submodule R M) := isNoetherian_of_fg_of_noetherian _ h
   isNoetherian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl)
 #align is_noetherian_of_fg_of_noetherian' isNoetherian_of_fg_of_noetherian'
 
-/- warning: is_noetherian_span_of_finite -> isNoetherian_span_of_finite is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {A : Set.{u2} M}, (Set.Finite.{u2} M A) -> (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 A)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 A)) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 A)))
-but is expected to have type
-  forall (R : Type.{u2}) {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)] {A : Set.{u1} M}, (Set.Finite.{u1} M A) -> (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 A))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 A)) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 A)))
-Case conversion may be inaccurate. Consider using '#align is_noetherian_span_of_finite isNoetherian_span_of_finiteₓ'. -/
 /-- In a module over a noetherian ring, the submodule generated by finitely many vectors is
 noetherian. -/
 theorem isNoetherian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R M]
@@ -760,12 +580,6 @@ theorem isNoetherian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R
   isNoetherian_of_fg_of_noetherian _ (Submodule.fg_def.mpr ⟨A, hA, rfl⟩)
 #align is_noetherian_span_of_finite isNoetherian_span_of_finite
 
-/- warning: is_noetherian_ring_of_surjective -> isNoetherianRing_of_surjective is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (S : Type.{u2}) [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))), (Function.Surjective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f)) -> (forall [H : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], IsNoetherianRing.{u2} S (Ring.toSemiring.{u2} S _inst_2))
-but is expected to have type
-  forall (R : Type.{u2}) [_inst_1 : Ring.{u2} R] (S : Type.{u1}) [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))), (Function.Surjective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2)))))) f)) -> (forall [H : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], IsNoetherianRing.{u1} S (Ring.toSemiring.{u1} S _inst_2))
-Case conversion may be inaccurate. Consider using '#align is_noetherian_ring_of_surjective isNoetherianRing_of_surjectiveₓ'. -/
 theorem isNoetherianRing_of_surjective (R) [Ring R] (S) [Ring S] (f : R →+* S)
     (hf : Function.Surjective f) [H : IsNoetherianRing R] : IsNoetherianRing S :=
   by
@@ -773,34 +587,16 @@ theorem isNoetherianRing_of_surjective (R) [Ring R] (S) [Ring S] (f : R →+* S)
   exact OrderEmbedding.wellFounded (Ideal.orderEmbeddingOfSurjective f hf).dual H
 #align is_noetherian_ring_of_surjective isNoetherianRing_of_surjective
 
-/- warning: is_noetherian_ring_range -> isNoetherianRing_range is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) [_inst_3 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], IsNoetherianRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subring.{u2} S _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subring.{u2} S _inst_2) S (Subring.setLike.{u2} S _inst_2)) (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subring.{u2} S _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subring.{u2} S _inst_2) S (Subring.setLike.{u2} S _inst_2)) (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f)) (Subring.toRing.{u2} S _inst_2 (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) [_inst_3 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], IsNoetherianRing.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subring.{u2} S _inst_2) (SetLike.instMembership.{u2, u2} (Subring.{u2} S _inst_2) S (Subring.instSetLikeSubring.{u2} S _inst_2)) x (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f))) (Subsemiring.toSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2) (Subring.toSubsemiring.{u2} S _inst_2 (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f)))
-Case conversion may be inaccurate. Consider using '#align is_noetherian_ring_range isNoetherianRing_rangeₓ'. -/
 instance isNoetherianRing_range {R} [Ring R] {S} [Ring S] (f : R →+* S) [IsNoetherianRing R] :
     IsNoetherianRing f.range :=
   isNoetherianRing_of_surjective R f.range f.range_restrict f.rangeRestrict_surjective
 #align is_noetherian_ring_range isNoetherianRing_range
 
-/- warning: is_noetherian_ring_of_ring_equiv -> isNoetherianRing_of_ringEquiv is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S], (RingEquiv.{u1, u2} R S (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1)) (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R _inst_1)) (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S _inst_2)) (Distrib.toHasAdd.{u2} S (Ring.toDistrib.{u2} S _inst_2))) -> (forall [_inst_3 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], IsNoetherianRing.{u2} S (Ring.toSemiring.{u2} S _inst_2))
-but is expected to have type
-  forall (R : Type.{u2}) [_inst_1 : Ring.{u2} R] {S : Type.{u1}} [_inst_2 : Ring.{u1} S], (RingEquiv.{u2, u1} R S (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2)))))) -> (forall [_inst_3 : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], IsNoetherianRing.{u1} S (Ring.toSemiring.{u1} S _inst_2))
-Case conversion may be inaccurate. Consider using '#align is_noetherian_ring_of_ring_equiv isNoetherianRing_of_ringEquivₓ'. -/
 theorem isNoetherianRing_of_ringEquiv (R) [Ring R] {S} [Ring S] (f : R ≃+* S) [IsNoetherianRing R] :
     IsNoetherianRing S :=
   isNoetherianRing_of_surjective R S f.toRingHom f.toEquiv.Surjective
 #align is_noetherian_ring_of_ring_equiv isNoetherianRing_of_ringEquiv
 
-/- warning: is_noetherian_ring.is_nilpotent_nilradical -> IsNoetherianRing.isNilpotent_nilradical is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], IsNilpotent.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroClass.toHasZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Monoid.Pow.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (nilradical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsNoetherianRing.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], IsNilpotent.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toCommMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemCommSemiring.toCommSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instIdemCommSemiringIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Monoid.Pow.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (nilradical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))
-Case conversion may be inaccurate. Consider using '#align is_noetherian_ring.is_nilpotent_nilradical IsNoetherianRing.isNilpotent_nilradicalₓ'. -/
 theorem IsNoetherianRing.isNilpotent_nilradical (R : Type _) [CommRing R] [IsNoetherianRing R] :
     IsNilpotent (nilradical R) :=
   by

210657c4

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -321,52 +321,28 @@ instance isNoetherian_pi {R ι : Type _} {M : ι → Type _} [Ring R] [∀ i, Ad
     exact fun f i =>
       Or.by_cases (Finset.mem_insert.1 i.2) (fun h : i.1 = a => show M i.1 from Eq.recOn h.symm f.1)
         fun h : i.1 ∈ s => show M i.1 from f.2 ⟨i.1, h⟩
-  · intro f g
-    ext i
-    unfold Or.by_cases
-    cases' i with i hi
+  · intro f g; ext i; unfold Or.by_cases; cases' i with i hi
     rcases Finset.mem_insert.1 hi with (rfl | h)
-    · change _ = _ + _
-      simp only [dif_pos]
-      rfl
-    · change _ = _ + _
-      have : ¬i = a := by
-        rintro rfl
-        exact has h
-      simp only [dif_neg this, dif_pos h]
-      rfl
-  · intro c f
-    ext i
-    unfold Or.by_cases
-    cases' i with i hi
+    · change _ = _ + _; simp only [dif_pos]; rfl
+    · change _ = _ + _; have : ¬i = a := by rintro rfl; exact has h
+      simp only [dif_neg this, dif_pos h]; rfl
+  · intro c f; ext i; unfold Or.by_cases; cases' i with i hi
     rcases Finset.mem_insert.1 hi with (rfl | h)
-    · change _ = c • _
-      simp only [dif_pos]
-      rfl
-    · change _ = c • _
-      have : ¬i = a := by
-        rintro rfl
-        exact has h
-      simp only [dif_neg this, dif_pos h]
-      rfl
+    · change _ = c • _; simp only [dif_pos]; rfl
+    · change _ = c • _; have : ¬i = a := by rintro rfl; exact has h
+      simp only [dif_neg this, dif_pos h]; rfl
   ·
     exact fun f =>
       (f ⟨a, Finset.mem_insert_self _ _⟩, fun i => f ⟨i.1, Finset.mem_insert_of_mem i.2⟩)
-  · intro f
-    apply Prod.ext
+  · intro f; apply Prod.ext
     · simp only [Or.by_cases, dif_pos]
     · ext ⟨i, his⟩
-      have : ¬i = a := by
-        rintro rfl
-        exact has his
+      have : ¬i = a := by rintro rfl; exact has his
       simp only [Or.by_cases, this, not_false_iff, dif_neg]
-  · intro f
-    ext ⟨i, hi⟩
+  · intro f; ext ⟨i, hi⟩
     rcases Finset.mem_insert.1 hi with (rfl | h)
     · simp only [Or.by_cases, dif_pos]
-    · have : ¬i = a := by
-        rintro rfl
-        exact has h
+    · have : ¬i = a := by rintro rfl; exact has h
       simp only [Or.by_cases, dif_neg this, dif_pos h]
 #align is_noetherian_pi isNoetherian_pi
 -/
@@ -438,8 +414,7 @@ theorem isNoetherian_iff_fg_wellFounded :
       rw [Eq]
       exact (le_sup_left : (R ∙ x) ≤ (R ∙ x) ⊔ N₀) (Submodule.mem_span_singleton_self _)
     · exact Submodule.FG.sup ⟨{x}, by rw [Finset.coe_singleton]⟩ h₁
-    · show N₀ ≤ (R ∙ x) ⊔ N₀
-      exact le_sup_right
+    · show N₀ ≤ (R ∙ x) ⊔ N₀; exact le_sup_right
     · exact sup_le ((Submodule.span_singleton_le_iff_mem _ _).mpr hx₁) e
 #align is_noetherian_iff_fg_well_founded isNoetherian_iff_fg_wellFounded
 
@@ -513,10 +488,7 @@ theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M
     by_contradiction fun hf =>
       (RelEmbedding.wellFounded_iff_no_descending_seq.1 (wellFounded_submodule_gt R M)).elim' _
   have f : ℕ ↪ s := Set.Infinite.natEmbedding s hf
-  have : ∀ n, coe ∘ f '' { m | m ≤ n } ⊆ s :=
-    by
-    rintro n x ⟨y, hy₁, rfl⟩
-    exact (f y).2
+  have : ∀ n, coe ∘ f '' { m | m ≤ n } ⊆ s := by rintro n x ⟨y, hy₁, rfl⟩; exact (f y).2
   have : ∀ a b : ℕ, a ≤ b ↔ span R (coe ∘ f '' { m | m ≤ a }) ≤ span R (coe ∘ f '' { m | m ≤ b }) :=
     by
     intro a b
@@ -745,19 +717,15 @@ theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module
     @isNoetherian_of_surjective ((↑s : Set M) → R) _ _ _ (Pi.module _ _ _) _ _ _ isNoetherian_pi
   · fapply LinearMap.mk
     · exact fun f => ⟨∑ i in s.attach, f i • i.1, N.sum_mem fun c _ => N.smul_mem _ <| this _ c.2⟩
-    · intro f g
-      apply Subtype.eq
+    · intro f g; apply Subtype.eq
       change (∑ i in s.attach, (f i + g i) • _) = _
-      simp only [add_smul, Finset.sum_add_distrib]
-      rfl
-    · intro c f
-      apply Subtype.eq
+      simp only [add_smul, Finset.sum_add_distrib]; rfl
+    · intro c f; apply Subtype.eq
       change (∑ i in s.attach, (c • f i) • _) = _
       simp only [smul_eq_mul, mul_smul]
       exact finset.smul_sum.symm
   rw [LinearMap.range_eq_top]
-  rintro ⟨n, hn⟩
-  change n ∈ N at hn
+  rintro ⟨n, hn⟩; change n ∈ N at hn
   rw [← hs, ← Set.image_id ↑s, Finsupp.mem_span_image_iff_total] at hn
   rcases hn with ⟨l, hl1, hl2⟩
   refine' ⟨fun x => l x, Subtype.ext _⟩

210657c4

bump to nightly-2023-05-28-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6c6011cf

Diff

@@ -530,10 +530,7 @@ theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M
 #align finite_of_linear_independent finite_of_linearIndependent
 
 /- warning: is_noetherian_of_range_eq_ker -> isNoetherian_of_range_eq_ker is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u2}} {M : Type.{u3}} {P : Type.{u4}} {N : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_6 : AddCommGroup.{u4} P] [_inst_7 : Module.{u2, u4} R P (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6)] [_inst_8 : IsNoetherian.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3] [_inst_9 : IsNoetherian.{u2, u4} R P (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_7] (f : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (g : LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7), (Function.Injective.{succ u3, succ u1} M N (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) => M -> N) (LinearMap.hasCoeToFun.{u2, u2, u3, u1} R R M N (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Surjective.{succ u1, succ u4} N P (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7) (fun (_x : LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u2, u2, u1, u4} R R N P (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) g)) -> (Eq.{succ u1} (Submodule.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5) (LinearMap.range.{u2, u2, u3, u1, max u3 u1} R R M N (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R M N (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) f) (LinearMap.ker.{u2, u2, u1, u4, max u1 u4} R R N P (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7) (LinearMap.semilinearMapClass.{u2, u2, u1, u4} R R N P (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) g)) -> (IsNoetherian.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5)
-but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u2}} {P : Type.{u1}} {N : Type.{u4}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u4} N] [_inst_5 : Module.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4)] [_inst_6 : AddCommGroup.{u1} P] [_inst_7 : Module.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6)] [_inst_8 : IsNoetherian.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] [_inst_9 : IsNoetherian.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_7] (f : LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (g : LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7), (Function.Injective.{succ u2, succ u4} M N (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f)) -> (Function.Surjective.{succ u4, succ u1} N P (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g)) -> (Eq.{succ u4} (Submodule.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5) (LinearMap.range.{u3, u3, u2, u4, max u4 u2} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (RingHomSurjective.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) f) (LinearMap.ker.{u3, u3, u4, u1, max u4 u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) (LinearMap.semilinearMapClass.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g)) -> (IsNoetherian.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5)
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_noetherian_of_range_eq_ker isNoetherian_of_range_eq_kerₓ'. -/
 /-- If the first and final modules in a short exact sequence are noetherian,
   then the middle module is also noetherian. -/
@@ -548,10 +545,7 @@ theorem isNoetherian_of_range_eq_ker [IsNoetherian R M] [IsNoetherian R P] (f :
 #align is_noetherian_of_range_eq_ker isNoetherian_of_range_eq_ker
 
 /- warning: is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot -> IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [I : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), Exists.{1} Nat (fun (n : Nat) => And (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Inf.inf.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f n)) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f n))) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))
-but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [I : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Exists.{1} Nat (fun (n : Nat) => And (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Inf.inf.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instInfSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (LinearMap.ker.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f n)) (LinearMap.range.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f n))) (Bot.bot.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_botₓ'. -/
 /-- For any endomorphism of a Noetherian module, there is some nontrivial iterate
 with disjoint kernel and range.

210657c4

bump to nightly-2023-05-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

fbc7b476

Diff

@@ -203,7 +203,7 @@ theorem isNoetherian_top_iff : IsNoetherian R (⊤ : Submodule R M) ↔ IsNoethe
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} P] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u1, u3} R P _inst_1 _inst_3 _inst_5] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u2, succ u3} M P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_4)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} P] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R P _inst_1 _inst_3 _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M P (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (IsNoetherian.{u3, u1} R M _inst_1 _inst_2 _inst_4)
+  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} P] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R P _inst_1 _inst_3 _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M P (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (IsNoetherian.{u3, u1} R M _inst_1 _inst_2 _inst_4)
 Case conversion may be inaccurate. Consider using '#align is_noetherian_of_injective isNoetherian_of_injectiveₓ'. -/
 theorem isNoetherian_of_injective [IsNoetherian R P] (f : M →ₗ[R] P) (hf : Function.Injective f) :
     IsNoetherian R M :=
@@ -214,7 +214,7 @@ theorem isNoetherian_of_injective [IsNoetherian R P] (f : M →ₗ[R] P) (hf : F
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} P] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u1, u3} R P _inst_1 _inst_3 _inst_5] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4} (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u2, succ u3} M P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} P] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R P _inst_1 _inst_3 _inst_5] {N : Submodule.{u3, u1} R M _inst_1 _inst_2 _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M P (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (Submodule.FG.{u3, u1} R M _inst_1 _inst_2 _inst_4 N)
+  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} P] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R P _inst_1 _inst_3 _inst_5] {N : Submodule.{u3, u1} R M _inst_1 _inst_2 _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M P (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (Submodule.FG.{u3, u1} R M _inst_1 _inst_2 _inst_4 N)
 Case conversion may be inaccurate. Consider using '#align fg_of_injective fg_of_injectiveₓ'. -/
 theorem fg_of_injective [IsNoetherian R P] {N : Submodule R M} (f : M →ₗ[R] P)
     (hf : Function.Injective f) : N.FG :=
@@ -244,7 +244,7 @@ variable {R M}
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u1, u3} R N _inst_1 _inst_3 _inst_5] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u2, succ u3} M N (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M N _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (Module.Finite.{u1, u2} R M _inst_1 _inst_2 _inst_4)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} N] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R N _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R N _inst_1 _inst_3 _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M N _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (Module.Finite.{u3, u1} R M _inst_1 _inst_2 _inst_4)
+  forall {R : Type.{u3}} {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} N] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R N _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R N _inst_1 _inst_3 _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M N _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (Module.Finite.{u3, u1} R M _inst_1 _inst_2 _inst_4)
 Case conversion may be inaccurate. Consider using '#align module.finite.of_injective Module.Finite.of_injectiveₓ'. -/
 theorem Finite.of_injective [IsNoetherian R N] (f : M →ₗ[R] N) (hf : Function.Injective f) :
     Finite R M :=
@@ -533,7 +533,7 @@ theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M
 lean 3 declaration is
   forall {R : Type.{u2}} {M : Type.{u3}} {P : Type.{u4}} {N : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_6 : AddCommGroup.{u4} P] [_inst_7 : Module.{u2, u4} R P (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6)] [_inst_8 : IsNoetherian.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3] [_inst_9 : IsNoetherian.{u2, u4} R P (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_7] (f : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (g : LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7), (Function.Injective.{succ u3, succ u1} M N (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) => M -> N) (LinearMap.hasCoeToFun.{u2, u2, u3, u1} R R M N (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Surjective.{succ u1, succ u4} N P (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7) (fun (_x : LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u2, u2, u1, u4} R R N P (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) g)) -> (Eq.{succ u1} (Submodule.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5) (LinearMap.range.{u2, u2, u3, u1, max u3 u1} R R M N (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R M N (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) f) (LinearMap.ker.{u2, u2, u1, u4, max u1 u4} R R N P (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7) (LinearMap.semilinearMapClass.{u2, u2, u1, u4} R R N P (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) g)) -> (IsNoetherian.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u2}} {P : Type.{u1}} {N : Type.{u4}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u4} N] [_inst_5 : Module.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4)] [_inst_6 : AddCommGroup.{u1} P] [_inst_7 : Module.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6)] [_inst_8 : IsNoetherian.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] [_inst_9 : IsNoetherian.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_7] (f : LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (g : LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7), (Function.Injective.{succ u2, succ u4} M N (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f)) -> (Function.Surjective.{succ u4, succ u1} N P (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g)) -> (Eq.{succ u4} (Submodule.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5) (LinearMap.range.{u3, u3, u2, u4, max u4 u2} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (RingHomSurjective.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) f) (LinearMap.ker.{u3, u3, u4, u1, max u4 u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) (LinearMap.semilinearMapClass.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g)) -> (IsNoetherian.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5)
+  forall {R : Type.{u3}} {M : Type.{u2}} {P : Type.{u1}} {N : Type.{u4}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u4} N] [_inst_5 : Module.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4)] [_inst_6 : AddCommGroup.{u1} P] [_inst_7 : Module.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6)] [_inst_8 : IsNoetherian.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] [_inst_9 : IsNoetherian.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_7] (f : LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (g : LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7), (Function.Injective.{succ u2, succ u4} M N (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f)) -> (Function.Surjective.{succ u4, succ u1} N P (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g)) -> (Eq.{succ u4} (Submodule.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5) (LinearMap.range.{u3, u3, u2, u4, max u4 u2} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (RingHomSurjective.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) f) (LinearMap.ker.{u3, u3, u4, u1, max u4 u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) (LinearMap.semilinearMapClass.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g)) -> (IsNoetherian.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5)
 Case conversion may be inaccurate. Consider using '#align is_noetherian_of_range_eq_ker isNoetherian_of_range_eq_kerₓ'. -/
 /-- If the first and final modules in a short exact sequence are noetherian,
   then the middle module is also noetherian. -/
@@ -579,7 +579,7 @@ theorem IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot [I : IsNoe
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Injective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Injective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Injective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
 Case conversion may be inaccurate. Consider using '#align is_noetherian.injective_of_surjective_endomorphism IsNoetherian.injective_of_surjective_endomorphismₓ'. -/
 /-- Any surjective endomorphism of a Noetherian module is injective. -/
 theorem IsNoetherian.injective_of_surjective_endomorphism [IsNoetherian R M] (f : M →ₗ[R] M)
@@ -595,7 +595,7 @@ theorem IsNoetherian.injective_of_surjective_endomorphism [IsNoetherian R M] (f
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Bijective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Bijective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Bijective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
 Case conversion may be inaccurate. Consider using '#align is_noetherian.bijective_of_surjective_endomorphism IsNoetherian.bijective_of_surjective_endomorphismₓ'. -/
 /-- Any surjective endomorphism of a Noetherian module is bijective. -/
 theorem IsNoetherian.bijective_of_surjective_endomorphism [IsNoetherian R M] (f : M →ₗ[R] M)
@@ -635,7 +635,7 @@ theorem IsNoetherian.disjoint_partialSups_eventually_bot [I : IsNoetherian R M]
 lean 3 declaration is
   forall {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_8 : IsNoetherian.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, max u3 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3), (Function.Injective.{max (succ u3) (succ u1), succ u3} (Prod.{u3, u1} M N) M (coeFn.{max (succ (max u3 u1)) (succ u3), max (succ (max u3 u1)) (succ u3)} (LinearMap.{u2, u2, max u3 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3) (fun (_x : LinearMap.{u2, u2, max u3 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3) => (Prod.{u3, u1} M N) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u3 u1, u3} R R (Prod.{u3, u1} M N) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (IsNoetherian.equivPunitOfProdInjective._proof_1.{u2} R _inst_1) (IsNoetherian.equivPunitOfProdInjective._proof_2.{u2} R _inst_1) N PUnit.{succ u1} (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} PUnit.{succ u1} PUnit.addCommGroup.{u1}) _inst_5 (PUnit.module.{u2, u1} R (Ring.toSemiring.{u2} R _inst_1)))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_8 : IsNoetherian.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, max u1 u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3), (Function.Injective.{max (succ u1) (succ u3), succ u3} (Prod.{u3, u1} M N) M (FunLike.coe.{max (succ u1) (succ u3), max (succ u1) (succ u3), succ u3} (LinearMap.{u2, u2, max u1 u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3) (Prod.{u3, u1} M N) (fun (_x : Prod.{u3, u1} M N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Prod.{u3, u1} M N) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u3, u3} R R (Prod.{u3, u1} M N) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) N PUnit.{succ u1} (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} PUnit.{succ u1} (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} PUnit.{succ u1} PUnit.linearOrderedCancelAddCommMonoid.{u1})) _inst_5 (PUnit.module.{u2, u1} R (Ring.toSemiring.{u2} R _inst_1)))
+  forall {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_8 : IsNoetherian.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, max u1 u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3), (Function.Injective.{max (succ u1) (succ u3), succ u3} (Prod.{u3, u1} M N) M (FunLike.coe.{max (succ u1) (succ u3), max (succ u1) (succ u3), succ u3} (LinearMap.{u2, u2, max u1 u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3) (Prod.{u3, u1} M N) (fun (_x : Prod.{u3, u1} M N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Prod.{u3, u1} M N) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u3, u3} R R (Prod.{u3, u1} M N) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) N PUnit.{succ u1} (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} PUnit.{succ u1} (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} PUnit.{succ u1} PUnit.linearOrderedCancelAddCommMonoid.{u1})) _inst_5 (PUnit.module.{u2, u1} R (Ring.toSemiring.{u2} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align is_noetherian.equiv_punit_of_prod_injective IsNoetherian.equivPunitOfProdInjectiveₓ'. -/
 /-- If `M ⊕ N` embeds into `M`, for `M` noetherian over `R`, then `N` is trivial.
 -/

210657c4

bump to nightly-2023-05-19-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

a31df521

Diff

@@ -802,7 +802,7 @@ theorem isNoetherian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (S : Type.{u2}) [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))), (Function.Surjective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f)) -> (forall [H : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], IsNoetherianRing.{u2} S (Ring.toSemiring.{u2} S _inst_2))
 but is expected to have type
-  forall (R : Type.{u2}) [_inst_1 : Ring.{u2} R] (S : Type.{u1}) [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))), (Function.Surjective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2)))))) f)) -> (forall [H : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], IsNoetherianRing.{u1} S (Ring.toSemiring.{u1} S _inst_2))
+  forall (R : Type.{u2}) [_inst_1 : Ring.{u2} R] (S : Type.{u1}) [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))), (Function.Surjective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2)))))) f)) -> (forall [H : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], IsNoetherianRing.{u1} S (Ring.toSemiring.{u1} S _inst_2))
 Case conversion may be inaccurate. Consider using '#align is_noetherian_ring_of_surjective isNoetherianRing_of_surjectiveₓ'. -/
 theorem isNoetherianRing_of_surjective (R) [Ring R] (S) [Ring S] (f : R →+* S)
     (hf : Function.Surjective f) [H : IsNoetherianRing R] : IsNoetherianRing S :=

210657c4

bump to nightly-2023-05-18-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

b46e9d53

Diff

@@ -165,7 +165,7 @@ variable (M)
 lean 3 declaration is
   forall {R : Type.{u1}} (M : Type.{u2}) {P : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} P] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R P _inst_1 _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Eq.{succ u3} (Submodule.{u1, u3} R P _inst_1 _inst_3 _inst_5) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) f) (Top.top.{u3} (Submodule.{u1, u3} R P _inst_1 _inst_3 _inst_5) (Submodule.hasTop.{u1, u3} R P _inst_1 _inst_3 _inst_5))) -> (forall [_inst_6 : IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_4], IsNoetherian.{u1, u3} R P _inst_1 _inst_3 _inst_5)
 but is expected to have type
-  forall {R : Type.{u3}} (M : Type.{u2}) {P : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} P] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u1} R P _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R P _inst_1 _inst_3 _inst_5) (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) f) (Top.top.{u1} (Submodule.{u3, u1} R P _inst_1 _inst_3 _inst_5) (Submodule.instTopSubmodule.{u3, u1} R P _inst_1 _inst_3 _inst_5))) -> (forall [_inst_6 : IsNoetherian.{u3, u2} R M _inst_1 _inst_2 _inst_4], IsNoetherian.{u3, u1} R P _inst_1 _inst_3 _inst_5)
+  forall {R : Type.{u3}} (M : Type.{u2}) {P : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} P] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u1} R P _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R P _inst_1 _inst_3 _inst_5) (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) f) (Top.top.{u1} (Submodule.{u3, u1} R P _inst_1 _inst_3 _inst_5) (Submodule.instTopSubmodule.{u3, u1} R P _inst_1 _inst_3 _inst_5))) -> (forall [_inst_6 : IsNoetherian.{u3, u2} R M _inst_1 _inst_2 _inst_4], IsNoetherian.{u3, u1} R P _inst_1 _inst_3 _inst_5)
 Case conversion may be inaccurate. Consider using '#align is_noetherian_of_surjective isNoetherian_of_surjectiveₓ'. -/
 theorem isNoetherian_of_surjective (f : M →ₗ[R] P) (hf : f.range = ⊤) [IsNoetherian R M] :
     IsNoetherian R P :=
@@ -203,7 +203,7 @@ theorem isNoetherian_top_iff : IsNoetherian R (⊤ : Submodule R M) ↔ IsNoethe
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} P] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u1, u3} R P _inst_1 _inst_3 _inst_5] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u2, succ u3} M P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_4)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} P] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R P _inst_1 _inst_3 _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M P (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (IsNoetherian.{u3, u1} R M _inst_1 _inst_2 _inst_4)
+  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} P] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R P _inst_1 _inst_3 _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M P (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (IsNoetherian.{u3, u1} R M _inst_1 _inst_2 _inst_4)
 Case conversion may be inaccurate. Consider using '#align is_noetherian_of_injective isNoetherian_of_injectiveₓ'. -/
 theorem isNoetherian_of_injective [IsNoetherian R P] (f : M →ₗ[R] P) (hf : Function.Injective f) :
     IsNoetherian R M :=
@@ -214,7 +214,7 @@ theorem isNoetherian_of_injective [IsNoetherian R P] (f : M →ₗ[R] P) (hf : F
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} P] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u1, u3} R P _inst_1 _inst_3 _inst_5] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4} (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u2, succ u3} M P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} P] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R P _inst_1 _inst_3 _inst_5] {N : Submodule.{u3, u1} R M _inst_1 _inst_2 _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M P (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (Submodule.FG.{u3, u1} R M _inst_1 _inst_2 _inst_4 N)
+  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} P] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R P _inst_1 _inst_3 _inst_5] {N : Submodule.{u3, u1} R M _inst_1 _inst_2 _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M P (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (Submodule.FG.{u3, u1} R M _inst_1 _inst_2 _inst_4 N)
 Case conversion may be inaccurate. Consider using '#align fg_of_injective fg_of_injectiveₓ'. -/
 theorem fg_of_injective [IsNoetherian R P] {N : Submodule R M} (f : M →ₗ[R] P)
     (hf : Function.Injective f) : N.FG :=
@@ -244,7 +244,7 @@ variable {R M}
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u1, u3} R N _inst_1 _inst_3 _inst_5] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u2, succ u3} M N (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M N _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (Module.Finite.{u1, u2} R M _inst_1 _inst_2 _inst_4)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} N] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R N _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R N _inst_1 _inst_3 _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M N _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (Module.Finite.{u3, u1} R M _inst_1 _inst_2 _inst_4)
+  forall {R : Type.{u3}} {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} N] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R N _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R N _inst_1 _inst_3 _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M N _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (Module.Finite.{u3, u1} R M _inst_1 _inst_2 _inst_4)
 Case conversion may be inaccurate. Consider using '#align module.finite.of_injective Module.Finite.of_injectiveₓ'. -/
 theorem Finite.of_injective [IsNoetherian R N] (f : M →ₗ[R] N) (hf : Function.Injective f) :
     Finite R M :=
@@ -269,7 +269,7 @@ include R
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_6 : IsNoetherian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5), (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) -> (IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : Module.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_6 : IsNoetherian.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.ker.{u3, u3, u1, u2, max u1 u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u1, u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f) (Bot.bot.{u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instBotSubmodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) -> (IsNoetherian.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)
+  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : Module.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_6 : IsNoetherian.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.ker.{u3, u3, u1, u2, max u1 u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u1, u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f) (Bot.bot.{u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instBotSubmodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) -> (IsNoetherian.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)
 Case conversion may be inaccurate. Consider using '#align is_noetherian_of_ker_bot isNoetherian_of_ker_botₓ'. -/
 theorem isNoetherian_of_ker_bot [IsNoetherian R P] (f : M →ₗ[R] P) (hf : f.ker = ⊥) :
     IsNoetherian R M :=
@@ -280,7 +280,7 @@ theorem isNoetherian_of_ker_bot [IsNoetherian R P] (f : M →ₗ[R] P) (hf : f.k
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_6 : IsNoetherian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5] {N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4} (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5), (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) -> (Submodule.FG.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : Module.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_6 : IsNoetherian.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_5] {N : Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.ker.{u3, u3, u1, u2, max u1 u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u1, u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f) (Bot.bot.{u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instBotSubmodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) -> (Submodule.FG.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 N)
+  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : Module.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_6 : IsNoetherian.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_5] {N : Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.ker.{u3, u3, u1, u2, max u1 u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u1, u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f) (Bot.bot.{u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instBotSubmodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) -> (Submodule.FG.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 N)
 Case conversion may be inaccurate. Consider using '#align fg_of_ker_bot fg_of_ker_botₓ'. -/
 theorem fg_of_ker_bot [IsNoetherian R P] {N : Submodule R M} (f : M →ₗ[R] P) (hf : f.ker = ⊥) :
     N.FG :=
@@ -533,7 +533,7 @@ theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M
 lean 3 declaration is
   forall {R : Type.{u2}} {M : Type.{u3}} {P : Type.{u4}} {N : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_6 : AddCommGroup.{u4} P] [_inst_7 : Module.{u2, u4} R P (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6)] [_inst_8 : IsNoetherian.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3] [_inst_9 : IsNoetherian.{u2, u4} R P (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_7] (f : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (g : LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7), (Function.Injective.{succ u3, succ u1} M N (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) => M -> N) (LinearMap.hasCoeToFun.{u2, u2, u3, u1} R R M N (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Surjective.{succ u1, succ u4} N P (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7) (fun (_x : LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u2, u2, u1, u4} R R N P (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) g)) -> (Eq.{succ u1} (Submodule.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5) (LinearMap.range.{u2, u2, u3, u1, max u3 u1} R R M N (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R M N (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) f) (LinearMap.ker.{u2, u2, u1, u4, max u1 u4} R R N P (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7) (LinearMap.semilinearMapClass.{u2, u2, u1, u4} R R N P (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) g)) -> (IsNoetherian.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u2}} {P : Type.{u1}} {N : Type.{u4}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u4} N] [_inst_5 : Module.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4)] [_inst_6 : AddCommGroup.{u1} P] [_inst_7 : Module.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6)] [_inst_8 : IsNoetherian.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] [_inst_9 : IsNoetherian.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_7] (f : LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (g : LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7), (Function.Injective.{succ u2, succ u4} M N (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f)) -> (Function.Surjective.{succ u4, succ u1} N P (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g)) -> (Eq.{succ u4} (Submodule.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5) (LinearMap.range.{u3, u3, u2, u4, max u4 u2} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (RingHomSurjective.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) f) (LinearMap.ker.{u3, u3, u4, u1, max u4 u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g)) -> (IsNoetherian.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5)
+  forall {R : Type.{u3}} {M : Type.{u2}} {P : Type.{u1}} {N : Type.{u4}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u4} N] [_inst_5 : Module.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4)] [_inst_6 : AddCommGroup.{u1} P] [_inst_7 : Module.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6)] [_inst_8 : IsNoetherian.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] [_inst_9 : IsNoetherian.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_7] (f : LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (g : LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7), (Function.Injective.{succ u2, succ u4} M N (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f)) -> (Function.Surjective.{succ u4, succ u1} N P (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g)) -> (Eq.{succ u4} (Submodule.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5) (LinearMap.range.{u3, u3, u2, u4, max u4 u2} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (RingHomSurjective.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) f) (LinearMap.ker.{u3, u3, u4, u1, max u4 u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) (LinearMap.semilinearMapClass.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g)) -> (IsNoetherian.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5)
 Case conversion may be inaccurate. Consider using '#align is_noetherian_of_range_eq_ker isNoetherian_of_range_eq_kerₓ'. -/
 /-- If the first and final modules in a short exact sequence are noetherian,
   then the middle module is also noetherian. -/
@@ -551,7 +551,7 @@ theorem isNoetherian_of_range_eq_ker [IsNoetherian R M] [IsNoetherian R P] (f :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [I : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), Exists.{1} Nat (fun (n : Nat) => And (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Inf.inf.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f n)) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f n))) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [I : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Exists.{1} Nat (fun (n : Nat) => And (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Inf.inf.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instInfSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (LinearMap.ker.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f n)) (LinearMap.range.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f n))) (Bot.bot.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [I : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Exists.{1} Nat (fun (n : Nat) => And (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Inf.inf.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instInfSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (LinearMap.ker.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f n)) (LinearMap.range.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f n))) (Bot.bot.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))
 Case conversion may be inaccurate. Consider using '#align is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_botₓ'. -/
 /-- For any endomorphism of a Noetherian module, there is some nontrivial iterate
 with disjoint kernel and range.
@@ -579,7 +579,7 @@ theorem IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot [I : IsNoe
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Injective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Injective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Injective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
 Case conversion may be inaccurate. Consider using '#align is_noetherian.injective_of_surjective_endomorphism IsNoetherian.injective_of_surjective_endomorphismₓ'. -/
 /-- Any surjective endomorphism of a Noetherian module is injective. -/
 theorem IsNoetherian.injective_of_surjective_endomorphism [IsNoetherian R M] (f : M →ₗ[R] M)
@@ -595,7 +595,7 @@ theorem IsNoetherian.injective_of_surjective_endomorphism [IsNoetherian R M] (f
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Bijective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Bijective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Bijective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
 Case conversion may be inaccurate. Consider using '#align is_noetherian.bijective_of_surjective_endomorphism IsNoetherian.bijective_of_surjective_endomorphismₓ'. -/
 /-- Any surjective endomorphism of a Noetherian module is bijective. -/
 theorem IsNoetherian.bijective_of_surjective_endomorphism [IsNoetherian R M] (f : M →ₗ[R] M)
@@ -635,7 +635,7 @@ theorem IsNoetherian.disjoint_partialSups_eventually_bot [I : IsNoetherian R M]
 lean 3 declaration is
   forall {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_8 : IsNoetherian.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, max u3 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3), (Function.Injective.{max (succ u3) (succ u1), succ u3} (Prod.{u3, u1} M N) M (coeFn.{max (succ (max u3 u1)) (succ u3), max (succ (max u3 u1)) (succ u3)} (LinearMap.{u2, u2, max u3 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3) (fun (_x : LinearMap.{u2, u2, max u3 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3) => (Prod.{u3, u1} M N) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u3 u1, u3} R R (Prod.{u3, u1} M N) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (IsNoetherian.equivPunitOfProdInjective._proof_1.{u2} R _inst_1) (IsNoetherian.equivPunitOfProdInjective._proof_2.{u2} R _inst_1) N PUnit.{succ u1} (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} PUnit.{succ u1} PUnit.addCommGroup.{u1}) _inst_5 (PUnit.module.{u2, u1} R (Ring.toSemiring.{u2} R _inst_1)))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_8 : IsNoetherian.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, max u1 u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3), (Function.Injective.{max (succ u1) (succ u3), succ u3} (Prod.{u3, u1} M N) M (FunLike.coe.{max (succ u1) (succ u3), max (succ u1) (succ u3), succ u3} (LinearMap.{u2, u2, max u1 u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3) (Prod.{u3, u1} M N) (fun (_x : Prod.{u3, u1} M N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Prod.{u3, u1} M N) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u3, u3} R R (Prod.{u3, u1} M N) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) N PUnit.{succ u1} (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} PUnit.{succ u1} (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} PUnit.{succ u1} PUnit.linearOrderedCancelAddCommMonoid.{u1})) _inst_5 (PUnit.module.{u2, u1} R (Ring.toSemiring.{u2} R _inst_1)))
+  forall {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_8 : IsNoetherian.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, max u1 u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3), (Function.Injective.{max (succ u1) (succ u3), succ u3} (Prod.{u3, u1} M N) M (FunLike.coe.{max (succ u1) (succ u3), max (succ u1) (succ u3), succ u3} (LinearMap.{u2, u2, max u1 u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3) (Prod.{u3, u1} M N) (fun (_x : Prod.{u3, u1} M N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Prod.{u3, u1} M N) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u3, u3} R R (Prod.{u3, u1} M N) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) N PUnit.{succ u1} (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} PUnit.{succ u1} (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} PUnit.{succ u1} PUnit.linearOrderedCancelAddCommMonoid.{u1})) _inst_5 (PUnit.module.{u2, u1} R (Ring.toSemiring.{u2} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align is_noetherian.equiv_punit_of_prod_injective IsNoetherian.equivPunitOfProdInjectiveₓ'. -/
 /-- If `M ⊕ N` embeds into `M`, for `M` noetherian over `R`, then `N` is trivial.
 -/

210657c4

bump to nightly-2023-05-16-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

9cb92e8c

Diff

@@ -101,7 +101,7 @@ theorem isNoetherian_def : IsNoetherian R M ↔ ∀ s : Submodule R M, s.FG :=
 
 /- warning: is_noetherian_submodule -> isNoetherian_submodule is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_4))))) s N) -> (Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_4 s))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_4))))) s N) -> (Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_4 s))
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x N)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_4))))) s N) -> (Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_4 s))
 Case conversion may be inaccurate. Consider using '#align is_noetherian_submodule isNoetherian_submoduleₓ'. -/
@@ -150,7 +150,7 @@ instance isNoetherian_submodule' [IsNoetherian R M] (N : Submodule R M) : IsNoet
 
 /- warning: is_noetherian_of_le -> isNoetherian_of_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4} {t : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4} [ht : IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) t) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 t) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 t)], (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_4))))) s t) -> (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) s) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 s) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 s))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4} {t : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4} [ht : IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) t) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 t) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 t)], (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_4))))) s t) -> (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) s) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 s) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 s))
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4} {t : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4} [ht : IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x t)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 t) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 t)], (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_4))))) s t) -> (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x s)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 s) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 s))
 Case conversion may be inaccurate. Consider using '#align is_noetherian_of_le isNoetherian_of_leₓ'. -/
@@ -394,7 +394,7 @@ variable {R M P : Type _} {N : Type w} [Semiring R] [AddCommMonoid M] [Module R
 
 /- warning: is_noetherian_iff_well_founded -> isNoetherian_iff_wellFounded is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (GT.gt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (GT.gt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))))))
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2236 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.RingTheory.Noetherian._hyg.2238 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => GT.gt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.RingTheory.Noetherian._hyg.2236 x._@.Mathlib.RingTheory.Noetherian._hyg.2238))
 Case conversion may be inaccurate. Consider using '#align is_noetherian_iff_well_founded isNoetherian_iff_wellFoundedₓ'. -/
@@ -409,7 +409,7 @@ theorem isNoetherian_iff_wellFounded :
 
 /- warning: is_noetherian_iff_fg_well_founded -> isNoetherian_iff_fg_wellFounded is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_3 N)) (GT.gt.{u2} (Subtype.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_3 N)) (Subtype.hasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_3 N))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_3 N)) (GT.gt.{u2} (Subtype.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_3 N)) (Subtype.hasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_3 N))))
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u1} (Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2445 : Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (x._@.Mathlib.RingTheory.Noetherian._hyg.2447 : Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) => GT.gt.{u1} (Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (Subtype.lt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) x._@.Mathlib.RingTheory.Noetherian._hyg.2445 x._@.Mathlib.RingTheory.Noetherian._hyg.2447))
 Case conversion may be inaccurate. Consider using '#align is_noetherian_iff_fg_well_founded isNoetherian_iff_fg_wellFoundedₓ'. -/
@@ -447,7 +447,7 @@ variable (R M)
 
 /- warning: well_founded_submodule_gt -> wellFounded_submodule_gt is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_8 : Semiring.{u1} R] [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} R M _inst_8 _inst_9] [_inst_11 : IsNoetherian.{u1, u2} R M _inst_8 _inst_9 _inst_10], WellFounded.{succ u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (GT.gt.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (Submodule.completeLattice.{u1, u2} R M _inst_8 _inst_9 _inst_10))))))
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_8 : Semiring.{u1} R] [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} R M _inst_8 _inst_9] [_inst_11 : IsNoetherian.{u1, u2} R M _inst_8 _inst_9 _inst_10], WellFounded.{succ u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (GT.gt.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (Submodule.completeLattice.{u1, u2} R M _inst_8 _inst_9 _inst_10))))))
 but is expected to have type
   forall (R : Type.{u2}) (M : Type.{u1}) [_inst_8 : Semiring.{u2} R] [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} R M _inst_8 _inst_9] [_inst_11 : IsNoetherian.{u2, u1} R M _inst_8 _inst_9 _inst_10], WellFounded.{succ u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2840 : Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (x._@.Mathlib.RingTheory.Noetherian._hyg.2842 : Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) => GT.gt.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (Submodule.completeLattice.{u2, u1} R M _inst_8 _inst_9 _inst_10))))) x._@.Mathlib.RingTheory.Noetherian._hyg.2840 x._@.Mathlib.RingTheory.Noetherian._hyg.2842)
 Case conversion may be inaccurate. Consider using '#align well_founded_submodule_gt wellFounded_submodule_gtₓ'. -/
@@ -460,7 +460,7 @@ variable {R M}
 
 /- warning: set_has_maximal_iff_noetherian -> set_has_maximal_iff_noetherian is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (forall (a : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) a) -> (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (M' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{0} (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) => forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) I a) -> (Not (LT.lt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) M' I)))))) (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (forall (a : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) a) -> (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (M' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{0} (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) => forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) I a) -> (Not (LT.lt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) M' I)))))) (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3)
 but is expected to have type
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (forall (a : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) a) -> (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (M' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => And (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) (forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) I a) -> (Not (LT.lt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) M' I)))))) (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3)
 Case conversion may be inaccurate. Consider using '#align set_has_maximal_iff_noetherian set_has_maximal_iff_noetherianₓ'. -/
@@ -481,7 +481,7 @@ theorem monotone_stabilizes_iff_noetherian :
 
 /- warning: is_noetherian.induction -> IsNoetherian.induction is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_8 : IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3] {P : (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) -> Prop}, (forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (forall (J : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (GT.gt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) J I) -> (P J)) -> (P I)) -> (forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), P I)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_8 : IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3] {P : (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) -> Prop}, (forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (forall (J : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (GT.gt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) J I) -> (P J)) -> (P I)) -> (forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), P I)
 but is expected to have type
   forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] [_inst_8 : IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3] {P : (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) -> Prop}, (forall (I : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), (forall (J : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), (GT.gt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) J I) -> (P J)) -> (P I)) -> (forall (I : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), P I)
 Case conversion may be inaccurate. Consider using '#align is_noetherian.induction IsNoetherian.inductionₓ'. -/

210657c4

bump to nightly-2023-05-16-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

7f411d29

Diff

@@ -72,7 +72,7 @@ open BigOperators Pointwise
 implemented as the predicate that all `R`-submodules of `M` are finitely generated.
 -/
 class IsNoetherian (R M) [Semiring R] [AddCommMonoid M] [Module R M] : Prop where
-  noetherian : ∀ s : Submodule R M, s.Fg
+  noetherian : ∀ s : Submodule R M, s.FG
 #align is_noetherian IsNoetherian
 -/
 
@@ -90,23 +90,23 @@ include R
 
 /- warning: is_noetherian_def -> isNoetherian_def is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_4) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_4 s)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_4) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_4 s)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_4) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_4 s)
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_4) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_4 s)
 Case conversion may be inaccurate. Consider using '#align is_noetherian_def isNoetherian_defₓ'. -/
 /-- An R-module is Noetherian iff all its submodules are finitely-generated. -/
-theorem isNoetherian_def : IsNoetherian R M ↔ ∀ s : Submodule R M, s.Fg :=
+theorem isNoetherian_def : IsNoetherian R M ↔ ∀ s : Submodule R M, s.FG :=
   ⟨fun h => h.noetherian, IsNoetherian.mk⟩
 #align is_noetherian_def isNoetherian_def
 
 /- warning: is_noetherian_submodule -> isNoetherian_submodule is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_4))))) s N) -> (Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_4 s))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_4))))) s N) -> (Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_4 s))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x N)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_4))))) s N) -> (Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_4 s))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x N)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_4))))) s N) -> (Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_4 s))
 Case conversion may be inaccurate. Consider using '#align is_noetherian_submodule isNoetherian_submoduleₓ'. -/
 theorem isNoetherian_submodule {N : Submodule R M} :
-    IsNoetherian R N ↔ ∀ s : Submodule R M, s ≤ N → s.Fg :=
+    IsNoetherian R N ↔ ∀ s : Submodule R M, s ≤ N → s.FG :=
   by
   refine'
     ⟨fun ⟨hn⟩ => fun s hs =>
@@ -122,23 +122,23 @@ theorem isNoetherian_submodule {N : Submodule R M} :
 
 /- warning: is_noetherian_submodule_left -> isNoetherian_submodule_left is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_2 _inst_4) N s))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_2 _inst_4) N s))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x N)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.instInfSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) N s))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x N)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.instInfSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) N s))
 Case conversion may be inaccurate. Consider using '#align is_noetherian_submodule_left isNoetherian_submodule_leftₓ'. -/
 theorem isNoetherian_submodule_left {N : Submodule R M} :
-    IsNoetherian R N ↔ ∀ s : Submodule R M, (N ⊓ s).Fg :=
+    IsNoetherian R N ↔ ∀ s : Submodule R M, (N ⊓ s).FG :=
   isNoetherian_submodule.trans ⟨fun H s => H _ inf_le_left, fun H s hs => inf_of_le_right hs ▸ H _⟩
 #align is_noetherian_submodule_left isNoetherian_submodule_left
 
 /- warning: is_noetherian_submodule_right -> isNoetherian_submodule_right is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_2 _inst_4) s N))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_2 _inst_4) s N))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x N)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.instInfSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) s N))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x N)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.instInfSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) s N))
 Case conversion may be inaccurate. Consider using '#align is_noetherian_submodule_right isNoetherian_submodule_rightₓ'. -/
 theorem isNoetherian_submodule_right {N : Submodule R M} :
-    IsNoetherian R N ↔ ∀ s : Submodule R M, (s ⊓ N).Fg :=
+    IsNoetherian R N ↔ ∀ s : Submodule R M, (s ⊓ N).FG :=
   isNoetherian_submodule.trans ⟨fun H s => H _ inf_le_right, fun H s hs => inf_of_le_left hs ▸ H _⟩
 #align is_noetherian_submodule_right isNoetherian_submodule_right
 
@@ -212,12 +212,12 @@ theorem isNoetherian_of_injective [IsNoetherian R P] (f : M →ₗ[R] P) (hf : F
 
 /- warning: fg_of_injective -> fg_of_injective is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} P] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u1, u3} R P _inst_1 _inst_3 _inst_5] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4} (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u2, succ u3} M P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)
+  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} P] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u1, u3} R P _inst_1 _inst_3 _inst_5] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4} (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u2, succ u3} M P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} P] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R P _inst_1 _inst_3 _inst_5] {N : Submodule.{u3, u1} R M _inst_1 _inst_2 _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M P (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (Submodule.Fg.{u3, u1} R M _inst_1 _inst_2 _inst_4 N)
+  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} P] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R P _inst_1 _inst_3 _inst_5] {N : Submodule.{u3, u1} R M _inst_1 _inst_2 _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M P (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (Submodule.FG.{u3, u1} R M _inst_1 _inst_2 _inst_4 N)
 Case conversion may be inaccurate. Consider using '#align fg_of_injective fg_of_injectiveₓ'. -/
 theorem fg_of_injective [IsNoetherian R P] {N : Submodule R M} (f : M →ₗ[R] P)
-    (hf : Function.Injective f) : N.Fg :=
+    (hf : Function.Injective f) : N.FG :=
   @IsNoetherian.noetherian _ _ _ (isNoetherian_of_injective f hf) N
 #align fg_of_injective fg_of_injective
 
@@ -278,12 +278,12 @@ theorem isNoetherian_of_ker_bot [IsNoetherian R P] (f : M →ₗ[R] P) (hf : f.k
 
 /- warning: fg_of_ker_bot -> fg_of_ker_bot is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_6 : IsNoetherian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5] {N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4} (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5), (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) -> (Submodule.Fg.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N)
+  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_6 : IsNoetherian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5] {N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4} (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5), (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) -> (Submodule.FG.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : Module.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_6 : IsNoetherian.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_5] {N : Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.ker.{u3, u3, u1, u2, max u1 u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u1, u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f) (Bot.bot.{u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instBotSubmodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) -> (Submodule.Fg.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 N)
+  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : Module.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_6 : IsNoetherian.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_5] {N : Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.ker.{u3, u3, u1, u2, max u1 u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u1, u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f) (Bot.bot.{u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instBotSubmodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) -> (Submodule.FG.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 N)
 Case conversion may be inaccurate. Consider using '#align fg_of_ker_bot fg_of_ker_botₓ'. -/
 theorem fg_of_ker_bot [IsNoetherian R P] {N : Submodule R M} (f : M →ₗ[R] P) (hf : f.ker = ⊥) :
-    N.Fg :=
+    N.FG :=
   @IsNoetherian.noetherian _ _ _ (isNoetherian_of_ker_bot f hf) N
 #align fg_of_ker_bot fg_of_ker_bot
 
@@ -409,16 +409,16 @@ theorem isNoetherian_iff_wellFounded :
 
 /- warning: is_noetherian_iff_fg_well_founded -> isNoetherian_iff_fg_wellFounded is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_3 N)) (GT.gt.{u2} (Subtype.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_3 N)) (Subtype.hasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_3 N))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_3 N)) (GT.gt.{u2} (Subtype.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_3 N)) (Subtype.hasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u1, u2} R M _inst_1 _inst_2 _inst_3 N))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u1} (Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2445 : Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (x._@.Mathlib.RingTheory.Noetherian._hyg.2447 : Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) => GT.gt.{u1} (Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (Subtype.lt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) x._@.Mathlib.RingTheory.Noetherian._hyg.2445 x._@.Mathlib.RingTheory.Noetherian._hyg.2447))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u1} (Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2445 : Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (x._@.Mathlib.RingTheory.Noetherian._hyg.2447 : Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) => GT.gt.{u1} (Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (Subtype.lt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.FG.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) x._@.Mathlib.RingTheory.Noetherian._hyg.2445 x._@.Mathlib.RingTheory.Noetherian._hyg.2447))
 Case conversion may be inaccurate. Consider using '#align is_noetherian_iff_fg_well_founded isNoetherian_iff_fg_wellFoundedₓ'. -/
 theorem isNoetherian_iff_fg_wellFounded :
     IsNoetherian R M ↔
       WellFounded
-        ((· > ·) : { N : Submodule R M // N.Fg } → { N : Submodule R M // N.Fg } → Prop) :=
+        ((· > ·) : { N : Submodule R M // N.FG } → { N : Submodule R M // N.FG } → Prop) :=
   by
-  let α := { N : Submodule R M // N.Fg }
+  let α := { N : Submodule R M // N.FG }
   constructor
   · intro H
     let f : α ↪o Submodule R M := OrderEmbedding.subtype _
@@ -437,7 +437,7 @@ theorem isNoetherian_iff_fg_wellFounded :
     · injection this with eq
       rw [Eq]
       exact (le_sup_left : (R ∙ x) ≤ (R ∙ x) ⊔ N₀) (Submodule.mem_span_singleton_self _)
-    · exact Submodule.Fg.sup ⟨{x}, by rw [Finset.coe_singleton]⟩ h₁
+    · exact Submodule.FG.sup ⟨{x}, by rw [Finset.coe_singleton]⟩ h₁
     · show N₀ ≤ (R ∙ x) ⊔ N₀
       exact le_sup_right
     · exact sup_le ((Submodule.span_singleton_le_iff_mem _ _).mpr hx₁) e
@@ -673,7 +673,7 @@ theorem isNoetherianRing_iff {R} [Semiring R] : IsNoetherianRing R ↔ IsNoether
 #print isNoetherianRing_iff_ideal_fg /-
 /-- A ring is Noetherian if and only if all its ideals are finitely-generated. -/
 theorem isNoetherianRing_iff_ideal_fg (R : Type _) [Semiring R] :
-    IsNoetherianRing R ↔ ∀ I : Ideal R, I.Fg :=
+    IsNoetherianRing R ↔ ∀ I : Ideal R, I.FG :=
   isNoetherianRing_iff.trans isNoetherian_def
 #align is_noetherian_ring_iff_ideal_fg isNoetherianRing_iff_ideal_fg
 -/
@@ -735,12 +735,12 @@ theorem isNoetherian_of_tower (R) {S M} [Semiring R] [Semiring S] [AddCommMonoid
 
 /- warning: is_noetherian_of_fg_of_noetherian -> isNoetherian_of_fg_of_noetherian is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_4 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], (Submodule.Fg.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 N) -> (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) N) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 N) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 N))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_4 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], (Submodule.FG.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 N) -> (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) N) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 N) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 N))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (N : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) [_inst_4 : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], (Submodule.Fg.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 N) -> (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x N)) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 N) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 N))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (N : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) [_inst_4 : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], (Submodule.FG.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 N) -> (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x N)) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 N) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 N))
 Case conversion may be inaccurate. Consider using '#align is_noetherian_of_fg_of_noetherian isNoetherian_of_fg_of_noetherianₓ'. -/
 theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module R M]
-    (N : Submodule R M) [IsNoetherianRing R] (hN : N.Fg) : IsNoetherian R N :=
+    (N : Submodule R M) [IsNoetherianRing R] (hN : N.FG) : IsNoetherian R N :=
   by
   let ⟨s, hs⟩ := hN
   haveI := Classical.decEq M
@@ -775,12 +775,12 @@ theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module
 
 /- warning: is_noetherian_of_fg_of_noetherian' -> isNoetherian_of_fg_of_noetherian' is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], (Submodule.Fg.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) -> (IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], (Submodule.FG.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) -> (IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], (Submodule.Fg.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) -> (IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], (Submodule.FG.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) -> (IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)
 Case conversion may be inaccurate. Consider using '#align is_noetherian_of_fg_of_noetherian' isNoetherian_of_fg_of_noetherian'ₓ'. -/
 theorem isNoetherian_of_fg_of_noetherian' {R M} [Ring R] [AddCommGroup M] [Module R M]
-    [IsNoetherianRing R] (h : (⊤ : Submodule R M).Fg) : IsNoetherian R M :=
+    [IsNoetherianRing R] (h : (⊤ : Submodule R M).FG) : IsNoetherian R M :=
   have : IsNoetherian R (⊤ : Submodule R M) := isNoetherian_of_fg_of_noetherian _ h
   isNoetherian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl)
 #align is_noetherian_of_fg_of_noetherian' isNoetherian_of_fg_of_noetherian'

210657c4

bump to nightly-2023-05-08-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

63e712c6

Diff

@@ -269,7 +269,7 @@ include R
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_6 : IsNoetherian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5), (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) -> (IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : Module.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_6 : IsNoetherian.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.ker.{u3, u3, u1, u2, max u1 u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u1, u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)))) f) (Bot.bot.{u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instBotSubmodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) -> (IsNoetherian.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)
+  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : Module.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_6 : IsNoetherian.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.ker.{u3, u3, u1, u2, max u1 u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u1, u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f) (Bot.bot.{u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instBotSubmodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) -> (IsNoetherian.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)
 Case conversion may be inaccurate. Consider using '#align is_noetherian_of_ker_bot isNoetherian_of_ker_botₓ'. -/
 theorem isNoetherian_of_ker_bot [IsNoetherian R P] (f : M →ₗ[R] P) (hf : f.ker = ⊥) :
     IsNoetherian R M :=
@@ -280,7 +280,7 @@ theorem isNoetherian_of_ker_bot [IsNoetherian R P] (f : M →ₗ[R] P) (hf : f.k
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_6 : IsNoetherian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5] {N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4} (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5), (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) -> (Submodule.Fg.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : Module.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_6 : IsNoetherian.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_5] {N : Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.ker.{u3, u3, u1, u2, max u1 u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u1, u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)))) f) (Bot.bot.{u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instBotSubmodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) -> (Submodule.Fg.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 N)
+  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : Module.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_6 : IsNoetherian.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_5] {N : Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.ker.{u3, u3, u1, u2, max u1 u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u1, u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f) (Bot.bot.{u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instBotSubmodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) -> (Submodule.Fg.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 N)
 Case conversion may be inaccurate. Consider using '#align fg_of_ker_bot fg_of_ker_botₓ'. -/
 theorem fg_of_ker_bot [IsNoetherian R P] {N : Submodule R M} (f : M →ₗ[R] P) (hf : f.ker = ⊥) :
     N.Fg :=
@@ -396,7 +396,7 @@ variable {R M P : Type _} {N : Type w} [Semiring R] [AddCommMonoid M] [Module R
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (GT.gt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2248 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.RingTheory.Noetherian._hyg.2250 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => GT.gt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.RingTheory.Noetherian._hyg.2248 x._@.Mathlib.RingTheory.Noetherian._hyg.2250))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2236 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.RingTheory.Noetherian._hyg.2238 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => GT.gt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.RingTheory.Noetherian._hyg.2236 x._@.Mathlib.RingTheory.Noetherian._hyg.2238))
 Case conversion may be inaccurate. Consider using '#align is_noetherian_iff_well_founded isNoetherian_iff_wellFoundedₓ'. -/
 theorem isNoetherian_iff_wellFounded :
     IsNoetherian R M ↔ WellFounded ((· > ·) : Submodule R M → Submodule R M → Prop) :=
@@ -411,7 +411,7 @@ theorem isNoetherian_iff_wellFounded :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_3 N)) (GT.gt.{u2} (Subtype.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_3 N)) (Subtype.hasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_3 N))))
 but is expected to have type
-  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u1} (Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2457 : Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (x._@.Mathlib.RingTheory.Noetherian._hyg.2459 : Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) => GT.gt.{u1} (Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (Subtype.lt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) x._@.Mathlib.RingTheory.Noetherian._hyg.2457 x._@.Mathlib.RingTheory.Noetherian._hyg.2459))
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u1} (Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2445 : Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (x._@.Mathlib.RingTheory.Noetherian._hyg.2447 : Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) => GT.gt.{u1} (Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (Subtype.lt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) x._@.Mathlib.RingTheory.Noetherian._hyg.2445 x._@.Mathlib.RingTheory.Noetherian._hyg.2447))
 Case conversion may be inaccurate. Consider using '#align is_noetherian_iff_fg_well_founded isNoetherian_iff_fg_wellFoundedₓ'. -/
 theorem isNoetherian_iff_fg_wellFounded :
     IsNoetherian R M ↔
@@ -449,7 +449,7 @@ variable (R M)
 lean 3 declaration is
   forall (R : Type.{u1}) (M : Type.{u2}) [_inst_8 : Semiring.{u1} R] [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} R M _inst_8 _inst_9] [_inst_11 : IsNoetherian.{u1, u2} R M _inst_8 _inst_9 _inst_10], WellFounded.{succ u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (GT.gt.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (Submodule.completeLattice.{u1, u2} R M _inst_8 _inst_9 _inst_10))))))
 but is expected to have type
-  forall (R : Type.{u2}) (M : Type.{u1}) [_inst_8 : Semiring.{u2} R] [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} R M _inst_8 _inst_9] [_inst_11 : IsNoetherian.{u2, u1} R M _inst_8 _inst_9 _inst_10], WellFounded.{succ u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2852 : Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (x._@.Mathlib.RingTheory.Noetherian._hyg.2854 : Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) => GT.gt.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (Submodule.completeLattice.{u2, u1} R M _inst_8 _inst_9 _inst_10))))) x._@.Mathlib.RingTheory.Noetherian._hyg.2852 x._@.Mathlib.RingTheory.Noetherian._hyg.2854)
+  forall (R : Type.{u2}) (M : Type.{u1}) [_inst_8 : Semiring.{u2} R] [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} R M _inst_8 _inst_9] [_inst_11 : IsNoetherian.{u2, u1} R M _inst_8 _inst_9 _inst_10], WellFounded.{succ u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2840 : Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (x._@.Mathlib.RingTheory.Noetherian._hyg.2842 : Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) => GT.gt.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (Submodule.completeLattice.{u2, u1} R M _inst_8 _inst_9 _inst_10))))) x._@.Mathlib.RingTheory.Noetherian._hyg.2840 x._@.Mathlib.RingTheory.Noetherian._hyg.2842)
 Case conversion may be inaccurate. Consider using '#align well_founded_submodule_gt wellFounded_submodule_gtₓ'. -/
 theorem wellFounded_submodule_gt (R M) [Semiring R] [AddCommMonoid M] [Module R M] :
     ∀ [IsNoetherian R M], WellFounded ((· > ·) : Submodule R M → Submodule R M → Prop) :=
@@ -533,7 +533,7 @@ theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M
 lean 3 declaration is
   forall {R : Type.{u2}} {M : Type.{u3}} {P : Type.{u4}} {N : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_6 : AddCommGroup.{u4} P] [_inst_7 : Module.{u2, u4} R P (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6)] [_inst_8 : IsNoetherian.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3] [_inst_9 : IsNoetherian.{u2, u4} R P (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_7] (f : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (g : LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7), (Function.Injective.{succ u3, succ u1} M N (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) => M -> N) (LinearMap.hasCoeToFun.{u2, u2, u3, u1} R R M N (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Surjective.{succ u1, succ u4} N P (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7) (fun (_x : LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u2, u2, u1, u4} R R N P (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) g)) -> (Eq.{succ u1} (Submodule.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5) (LinearMap.range.{u2, u2, u3, u1, max u3 u1} R R M N (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R M N (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) f) (LinearMap.ker.{u2, u2, u1, u4, max u1 u4} R R N P (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7) (LinearMap.semilinearMapClass.{u2, u2, u1, u4} R R N P (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) g)) -> (IsNoetherian.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5)
 but is expected to have type
-  forall {R : Type.{u3}} {M : Type.{u2}} {P : Type.{u1}} {N : Type.{u4}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u4} N] [_inst_5 : Module.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4)] [_inst_6 : AddCommGroup.{u1} P] [_inst_7 : Module.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6)] [_inst_8 : IsNoetherian.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] [_inst_9 : IsNoetherian.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_7] (f : LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (g : LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7), (Function.Injective.{succ u2, succ u4} M N (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)))) f)) -> (Function.Surjective.{succ u4, succ u1} N P (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)))) g)) -> (Eq.{succ u4} (Submodule.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5) (LinearMap.range.{u3, u3, u2, u4, max u4 u2} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)))) (RingHomSurjective.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) f) (LinearMap.ker.{u3, u3, u4, u1, max u4 u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)))) g)) -> (IsNoetherian.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5)
+  forall {R : Type.{u3}} {M : Type.{u2}} {P : Type.{u1}} {N : Type.{u4}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u4} N] [_inst_5 : Module.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4)] [_inst_6 : AddCommGroup.{u1} P] [_inst_7 : Module.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6)] [_inst_8 : IsNoetherian.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] [_inst_9 : IsNoetherian.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_7] (f : LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (g : LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7), (Function.Injective.{succ u2, succ u4} M N (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) f)) -> (Function.Surjective.{succ u4, succ u1} N P (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g)) -> (Eq.{succ u4} (Submodule.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5) (LinearMap.range.{u3, u3, u2, u4, max u4 u2} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) (RingHomSurjective.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) f) (LinearMap.ker.{u3, u3, u4, u1, max u4 u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (Ring.toSemiring.{u3} R _inst_1)))) g)) -> (IsNoetherian.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5)
 Case conversion may be inaccurate. Consider using '#align is_noetherian_of_range_eq_ker isNoetherian_of_range_eq_kerₓ'. -/
 /-- If the first and final modules in a short exact sequence are noetherian,
   then the middle module is also noetherian. -/
@@ -802,7 +802,7 @@ theorem isNoetherian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (S : Type.{u2}) [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))), (Function.Surjective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f)) -> (forall [H : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], IsNoetherianRing.{u2} S (Ring.toSemiring.{u2} S _inst_2))
 but is expected to have type
-  forall (R : Type.{u2}) [_inst_1 : Ring.{u2} R] (S : Type.{u1}) [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))), (Function.Surjective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2)))))) f)) -> (forall [H : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], IsNoetherianRing.{u1} S (Ring.toSemiring.{u1} S _inst_2))
+  forall (R : Type.{u2}) [_inst_1 : Ring.{u2} R] (S : Type.{u1}) [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))), (Function.Surjective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S _inst_2)))))) f)) -> (forall [H : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], IsNoetherianRing.{u1} S (Ring.toSemiring.{u1} S _inst_2))
 Case conversion may be inaccurate. Consider using '#align is_noetherian_ring_of_surjective isNoetherianRing_of_surjectiveₓ'. -/
 theorem isNoetherianRing_of_surjective (R) [Ring R] (S) [Ring S] (f : R →+* S)
     (hf : Function.Surjective f) [H : IsNoetherianRing R] : IsNoetherianRing S :=
@@ -815,7 +815,7 @@ theorem isNoetherianRing_of_surjective (R) [Ring R] (S) [Ring S] (f : R →+* S)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) [_inst_3 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], IsNoetherianRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subring.{u2} S _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subring.{u2} S _inst_2) S (Subring.setLike.{u2} S _inst_2)) (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subring.{u2} S _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subring.{u2} S _inst_2) S (Subring.setLike.{u2} S _inst_2)) (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f)) (Subring.toRing.{u2} S _inst_2 (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) [_inst_3 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], IsNoetherianRing.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subring.{u2} S _inst_2) (SetLike.instMembership.{u2, u2} (Subring.{u2} S _inst_2) S (Subring.instSetLikeSubring.{u2} S _inst_2)) x (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f))) (Ring.toSemiring.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subring.{u2} S _inst_2) (SetLike.instMembership.{u2, u2} (Subring.{u2} S _inst_2) S (Subring.instSetLikeSubring.{u2} S _inst_2)) x (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f))) (Subring.toRing.{u2} S _inst_2 (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) [_inst_3 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], IsNoetherianRing.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subring.{u2} S _inst_2) (SetLike.instMembership.{u2, u2} (Subring.{u2} S _inst_2) S (Subring.instSetLikeSubring.{u2} S _inst_2)) x (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f))) (Subsemiring.toSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2) (Subring.toSubsemiring.{u2} S _inst_2 (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f)))
 Case conversion may be inaccurate. Consider using '#align is_noetherian_ring_range isNoetherianRing_rangeₓ'. -/
 instance isNoetherianRing_range {R} [Ring R] {S} [Ring S] (f : R →+* S) [IsNoetherianRing R] :
     IsNoetherianRing f.range :=
@@ -837,7 +837,7 @@ theorem isNoetherianRing_of_ringEquiv (R) [Ring R] {S} [Ring S] (f : R ≃+* S)
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], IsNilpotent.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroClass.toHasZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Monoid.Pow.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (nilradical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], IsNilpotent.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toCommMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemCommSemiring.toCommSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instIdemCommSemiringIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Monoid.Pow.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (nilradical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsNoetherianRing.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], IsNilpotent.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toCommMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemCommSemiring.toCommSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instIdemCommSemiringIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Monoid.Pow.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (nilradical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))
 Case conversion may be inaccurate. Consider using '#align is_noetherian_ring.is_nilpotent_nilradical IsNoetherianRing.isNilpotent_nilradicalₓ'. -/
 theorem IsNoetherianRing.isNilpotent_nilradical (R : Type _) [CommRing R] [IsNoetherianRing R] :
     IsNilpotent (nilradical R) :=

210657c4

bump to nightly-2023-04-12-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

e13a7759

Diff

@@ -449,7 +449,7 @@ variable (R M)
 lean 3 declaration is
   forall (R : Type.{u1}) (M : Type.{u2}) [_inst_8 : Semiring.{u1} R] [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} R M _inst_8 _inst_9] [_inst_11 : IsNoetherian.{u1, u2} R M _inst_8 _inst_9 _inst_10], WellFounded.{succ u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (GT.gt.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (Submodule.completeLattice.{u1, u2} R M _inst_8 _inst_9 _inst_10))))))
 but is expected to have type
-  forall (R : Type.{u2}) (M : Type.{u1}) [_inst_8 : Semiring.{u2} R] [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} R M _inst_8 _inst_9] [_inst_11 : IsNoetherian.{u2, u1} R M _inst_8 _inst_9 _inst_10], WellFounded.{succ u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2938 : Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (x._@.Mathlib.RingTheory.Noetherian._hyg.2940 : Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) => GT.gt.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (Submodule.completeLattice.{u2, u1} R M _inst_8 _inst_9 _inst_10))))) x._@.Mathlib.RingTheory.Noetherian._hyg.2938 x._@.Mathlib.RingTheory.Noetherian._hyg.2940)
+  forall (R : Type.{u2}) (M : Type.{u1}) [_inst_8 : Semiring.{u2} R] [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} R M _inst_8 _inst_9] [_inst_11 : IsNoetherian.{u2, u1} R M _inst_8 _inst_9 _inst_10], WellFounded.{succ u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2852 : Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (x._@.Mathlib.RingTheory.Noetherian._hyg.2854 : Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) => GT.gt.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (Submodule.completeLattice.{u2, u1} R M _inst_8 _inst_9 _inst_10))))) x._@.Mathlib.RingTheory.Noetherian._hyg.2852 x._@.Mathlib.RingTheory.Noetherian._hyg.2854)
 Case conversion may be inaccurate. Consider using '#align well_founded_submodule_gt wellFounded_submodule_gtₓ'. -/
 theorem wellFounded_submodule_gt (R M) [Semiring R] [AddCommMonoid M] [Module R M] :
     ∀ [IsNoetherian R M], WellFounded ((· > ·) : Submodule R M → Submodule R M → Prop) :=
@@ -462,7 +462,7 @@ variable {R M}
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (forall (a : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) a) -> (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (M' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{0} (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) => forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) I a) -> (Not (LT.lt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) M' I)))))) (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3)
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (forall (a : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) a) -> (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (M' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => And (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) (forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) I a) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) M' I) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) I M'))))) (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (forall (a : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) a) -> (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (M' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => And (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) (forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) I a) -> (Not (LT.lt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) M' I)))))) (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3)
 Case conversion may be inaccurate. Consider using '#align set_has_maximal_iff_noetherian set_has_maximal_iff_noetherianₓ'. -/
 /-- A module is Noetherian iff every nonempty set of submodules has a maximal submodule among them.
 -/

210657c4

bump to nightly-2023-04-02-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/88fcb83fe7996142dfcfe7368d31304a9adc874a

a22ad38d

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Kevin Buzzard
 
 ! This file was ported from Lean 3 source module ring_theory.noetherian
-! leanprover-community/mathlib commit aa3a420527e0fbfd0f6615b95b761254a9166e12
+! leanprover-community/mathlib commit 210657c4ea4a4a7b234392f70a3a2a83346dfa90
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -427,21 +427,20 @@ theorem isNoetherian_iff_fg_wellFounded :
     constructor
     intro N
     obtain ⟨⟨N₀, h₁⟩, e : N₀ ≤ N, h₂⟩ :=
-      well_founded.well_founded_iff_has_max'.mp H { N' : α | N'.1 ≤ N }
-        ⟨⟨⊥, Submodule.fg_bot⟩, bot_le⟩
+      WellFounded.has_min H { N' : α | N'.1 ≤ N } ⟨⟨⊥, Submodule.fg_bot⟩, bot_le⟩
     convert h₁
     refine' (e.antisymm _).symm
     by_contra h₃
     obtain ⟨x, hx₁ : x ∈ N, hx₂ : x ∉ N₀⟩ := set.not_subset.mp h₃
     apply hx₂
-    have := h₂ ⟨(R ∙ x) ⊔ N₀, _⟩ _ _
+    have := eq_of_le_of_not_lt _ (h₂ ⟨(R ∙ x) ⊔ N₀, _⟩ _)
     · injection this with eq
-      rw [← Eq]
+      rw [Eq]
       exact (le_sup_left : (R ∙ x) ≤ (R ∙ x) ⊔ N₀) (Submodule.mem_span_singleton_self _)
     · exact Submodule.Fg.sup ⟨{x}, by rw [Finset.coe_singleton]⟩ h₁
-    · exact sup_le ((Submodule.span_singleton_le_iff_mem _ _).mpr hx₁) e
     · show N₀ ≤ (R ∙ x) ⊔ N₀
       exact le_sup_right
+    · exact sup_le ((Submodule.span_singleton_le_iff_mem _ _).mpr hx₁) e
 #align is_noetherian_iff_fg_well_founded isNoetherian_iff_fg_wellFounded
 
 variable (R M)
@@ -461,16 +460,15 @@ variable {R M}
 
 /- warning: set_has_maximal_iff_noetherian -> set_has_maximal_iff_noetherian is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (forall (a : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) a) -> (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (M' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{0} (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) => forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) I a) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) M' I) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) I M'))))) (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3)
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (forall (a : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) a) -> (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (M' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{0} (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) => forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) I a) -> (Not (LT.lt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) M' I)))))) (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3)
 but is expected to have type
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (forall (a : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) a) -> (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (M' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => And (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) (forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) I a) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) M' I) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) I M'))))) (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3)
 Case conversion may be inaccurate. Consider using '#align set_has_maximal_iff_noetherian set_has_maximal_iff_noetherianₓ'. -/
 /-- A module is Noetherian iff every nonempty set of submodules has a maximal submodule among them.
 -/
 theorem set_has_maximal_iff_noetherian :
-    (∀ a : Set <| Submodule R M, a.Nonempty → ∃ M' ∈ a, ∀ I ∈ a, M' ≤ I → I = M') ↔
-      IsNoetherian R M :=
-  by rw [isNoetherian_iff_wellFounded, WellFounded.wellFounded_iff_has_max']
+    (∀ a : Set <| Submodule R M, a.Nonempty → ∃ M' ∈ a, ∀ I ∈ a, ¬M' < I) ↔ IsNoetherian R M := by
+  rw [isNoetherian_iff_wellFounded, WellFounded.wellFounded_iff_has_min]
 #align set_has_maximal_iff_noetherian set_has_maximal_iff_noetherian
 
 #print monotone_stabilizes_iff_noetherian /-

aa3a4205

bump to nightly-2023-03-22-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/dd6388c44e6f6b4547070b887c5905d5cfe6c9f8

2e6ecab9

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Kevin Buzzard
 
 ! This file was ported from Lean 3 source module ring_theory.noetherian
-! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
+! leanprover-community/mathlib commit aa3a420527e0fbfd0f6615b95b761254a9166e12
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -21,6 +21,9 @@ import Mathbin.RingTheory.Nilpotent
 /-!
 # Noetherian rings and modules
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The following are equivalent for a module M over a ring R:
 1. Every increasing chain of submodules M₁ ⊆ M₂ ⊆ M₃ ⊆ ⋯ eventually stabilises.
 2. Every submodule is finitely generated.

da420a8c

bump to nightly-2023-03-20-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ec294687917cbc5c73620b4414ae9b5dd9ae1b4

06c3e345

Diff

@@ -64,12 +64,14 @@ open Set
 
 open BigOperators Pointwise
 
+#print IsNoetherian /-
 /-- `is_noetherian R M` is the proposition that `M` is a Noetherian `R`-module,
 implemented as the predicate that all `R`-submodules of `M` are finitely generated.
 -/
 class IsNoetherian (R M) [Semiring R] [AddCommMonoid M] [Module R M] : Prop where
   noetherian : ∀ s : Submodule R M, s.Fg
 #align is_noetherian IsNoetherian
+-/
 
 section
 
@@ -83,11 +85,23 @@ open IsNoetherian
 
 include R
 
+/- warning: is_noetherian_def -> isNoetherian_def is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_4) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_4 s)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_4) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_4 s)
+Case conversion may be inaccurate. Consider using '#align is_noetherian_def isNoetherian_defₓ'. -/
 /-- An R-module is Noetherian iff all its submodules are finitely-generated. -/
 theorem isNoetherian_def : IsNoetherian R M ↔ ∀ s : Submodule R M, s.Fg :=
   ⟨fun h => h.noetherian, IsNoetherian.mk⟩
 #align is_noetherian_def isNoetherian_def
 
+/- warning: is_noetherian_submodule -> isNoetherian_submodule is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_4))))) s N) -> (Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_4 s))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x N)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_4))))) s N) -> (Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_4 s))
+Case conversion may be inaccurate. Consider using '#align is_noetherian_submodule isNoetherian_submoduleₓ'. -/
 theorem isNoetherian_submodule {N : Submodule R M} :
     IsNoetherian R N ↔ ∀ s : Submodule R M, s ≤ N → s.Fg :=
   by
@@ -103,20 +117,40 @@ theorem isNoetherian_submodule {N : Submodule R M} :
   exact (Submodule.fg_top _).1 (h₂ ▸ h₃)
 #align is_noetherian_submodule isNoetherian_submodule
 
+/- warning: is_noetherian_submodule_left -> isNoetherian_submodule_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_2 _inst_4) N s))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x N)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.instInfSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) N s))
+Case conversion may be inaccurate. Consider using '#align is_noetherian_submodule_left isNoetherian_submodule_leftₓ'. -/
 theorem isNoetherian_submodule_left {N : Submodule R M} :
     IsNoetherian R N ↔ ∀ s : Submodule R M, (N ⊓ s).Fg :=
   isNoetherian_submodule.trans ⟨fun H s => H _ inf_le_left, fun H s hs => inf_of_le_right hs ▸ H _⟩
 #align is_noetherian_submodule_left isNoetherian_submodule_left
 
+/- warning: is_noetherian_submodule_right -> isNoetherian_submodule_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4), Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.hasInf.{u1, u2} R M _inst_1 _inst_2 _inst_4) s N))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4}, Iff (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x N)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 N) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 N)) (forall (s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4), Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_4 (Inf.inf.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.instInfSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) s N))
+Case conversion may be inaccurate. Consider using '#align is_noetherian_submodule_right isNoetherian_submodule_rightₓ'. -/
 theorem isNoetherian_submodule_right {N : Submodule R M} :
     IsNoetherian R N ↔ ∀ s : Submodule R M, (s ⊓ N).Fg :=
   isNoetherian_submodule.trans ⟨fun H s => H _ inf_le_right, fun H s hs => inf_of_le_left hs ▸ H _⟩
 #align is_noetherian_submodule_right isNoetherian_submodule_right
 
+#print isNoetherian_submodule' /-
 instance isNoetherian_submodule' [IsNoetherian R M] (N : Submodule R M) : IsNoetherian R N :=
   isNoetherian_submodule.2 fun _ _ => IsNoetherian.noetherian _
 #align is_noetherian_submodule' isNoetherian_submodule'
+-/
 
+/- warning: is_noetherian_of_le -> isNoetherian_of_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] {s : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4} {t : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4} [ht : IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) t) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 t) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 t)], (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_4))))) s t) -> (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) s) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 s) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 s))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2] {s : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4} {t : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4} [ht : IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x t)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 t) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 t)], (LE.le.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Preorder.toLE.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_4))))) s t) -> (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x s)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 s) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 s))
+Case conversion may be inaccurate. Consider using '#align is_noetherian_of_le isNoetherian_of_leₓ'. -/
 theorem isNoetherian_of_le {s t : Submodule R M} [ht : IsNoetherian R t] (h : s ≤ t) :
     IsNoetherian R s :=
   isNoetherian_submodule.mpr fun s' hs' => isNoetherian_submodule.mp ht _ (le_trans hs' h)
@@ -124,6 +158,12 @@ theorem isNoetherian_of_le {s t : Submodule R M} [ht : IsNoetherian R t] (h : s
 
 variable (M)
 
+/- warning: is_noetherian_of_surjective -> isNoetherian_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} (M : Type.{u2}) {P : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} P] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R P _inst_1 _inst_3] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Eq.{succ u3} (Submodule.{u1, u3} R P _inst_1 _inst_3 _inst_5) (LinearMap.range.{u1, u1, u2, u3, max u2 u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) f) (Top.top.{u3} (Submodule.{u1, u3} R P _inst_1 _inst_3 _inst_5) (Submodule.hasTop.{u1, u3} R P _inst_1 _inst_3 _inst_5))) -> (forall [_inst_6 : IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_4], IsNoetherian.{u1, u3} R P _inst_1 _inst_3 _inst_5)
+but is expected to have type
+  forall {R : Type.{u3}} (M : Type.{u2}) {P : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} P] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u1} R P _inst_1 _inst_3] (f : LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R P _inst_1 _inst_3 _inst_5) (LinearMap.range.{u3, u3, u2, u1, max u2 u1} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u1} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (RingHomSurjective.ids.{u3} R _inst_1) f) (Top.top.{u1} (Submodule.{u3, u1} R P _inst_1 _inst_3 _inst_5) (Submodule.instTopSubmodule.{u3, u1} R P _inst_1 _inst_3 _inst_5))) -> (forall [_inst_6 : IsNoetherian.{u3, u2} R M _inst_1 _inst_2 _inst_4], IsNoetherian.{u3, u1} R P _inst_1 _inst_3 _inst_5)
+Case conversion may be inaccurate. Consider using '#align is_noetherian_of_surjective isNoetherian_of_surjectiveₓ'. -/
 theorem isNoetherian_of_surjective (f : M →ₗ[R] P) (hf : f.range = ⊤) [IsNoetherian R M] :
     IsNoetherian R P :=
   ⟨fun s =>
@@ -133,10 +173,22 @@ theorem isNoetherian_of_surjective (f : M →ₗ[R] P) (hf : f.range = ⊤) [IsN
 
 variable {M}
 
+/- warning: is_noetherian_of_linear_equiv -> isNoetherian_of_linearEquiv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} P] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R P _inst_1 _inst_3], (LinearEquiv.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M P _inst_2 _inst_3 _inst_4 _inst_5) -> (forall [_inst_6 : IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_4], IsNoetherian.{u1, u3} R P _inst_1 _inst_3 _inst_5)
+but is expected to have type
+  forall {R : Type.{u3}} {M : Type.{u2}} {P : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u1} P] [_inst_4 : Module.{u3, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u1} R P _inst_1 _inst_3], (LinearEquiv.{u3, u3, u2, u1} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) M P _inst_2 _inst_3 _inst_4 _inst_5) -> (forall [_inst_6 : IsNoetherian.{u3, u2} R M _inst_1 _inst_2 _inst_4], IsNoetherian.{u3, u1} R P _inst_1 _inst_3 _inst_5)
+Case conversion may be inaccurate. Consider using '#align is_noetherian_of_linear_equiv isNoetherian_of_linearEquivₓ'. -/
 theorem isNoetherian_of_linearEquiv (f : M ≃ₗ[R] P) [IsNoetherian R M] : IsNoetherian R P :=
   isNoetherian_of_surjective _ f.toLinearMap f.range
 #align is_noetherian_of_linear_equiv isNoetherian_of_linearEquiv
 
+/- warning: is_noetherian_top_iff -> isNoetherian_top_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_4)) (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.hasTop.{u1, u2} R M _inst_1 _inst_2 _inst_4))) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_4 (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.hasTop.{u1, u2} R M _inst_1 _inst_2 _inst_4))) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_4 (Top.top.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4) (Submodule.hasTop.{u1, u2} R M _inst_1 _inst_2 _inst_4)))) (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_4)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_4 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_4)) x (Top.top.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_4)))) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_4 (Top.top.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_4))) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_4 (Top.top.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_4) (Submodule.instTopSubmodule.{u2, u1} R M _inst_1 _inst_2 _inst_4)))) (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_4)
+Case conversion may be inaccurate. Consider using '#align is_noetherian_top_iff isNoetherian_top_iffₓ'. -/
 theorem isNoetherian_top_iff : IsNoetherian R (⊤ : Submodule R M) ↔ IsNoetherian R M :=
   by
   constructor <;> intro h
@@ -144,11 +196,23 @@ theorem isNoetherian_top_iff : IsNoetherian R (⊤ : Submodule R M) ↔ IsNoethe
   · exact isNoetherian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl).symm
 #align is_noetherian_top_iff isNoetherian_top_iff
 
+/- warning: is_noetherian_of_injective -> isNoetherian_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} P] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u1, u3} R P _inst_1 _inst_3 _inst_5] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u2, succ u3} M P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_4)
+but is expected to have type
+  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} P] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R P _inst_1 _inst_3 _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M P (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (IsNoetherian.{u3, u1} R M _inst_1 _inst_2 _inst_4)
+Case conversion may be inaccurate. Consider using '#align is_noetherian_of_injective isNoetherian_of_injectiveₓ'. -/
 theorem isNoetherian_of_injective [IsNoetherian R P] (f : M →ₗ[R] P) (hf : Function.Injective f) :
     IsNoetherian R M :=
   isNoetherian_of_linearEquiv (LinearEquiv.ofInjective f hf).symm
 #align is_noetherian_of_injective isNoetherian_of_injective
 
+/- warning: fg_of_injective -> fg_of_injective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} P] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u1, u3} R P _inst_1 _inst_3 _inst_5] {N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_4} (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u2, succ u3} M P (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) => M -> P) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_4 N)
+but is expected to have type
+  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} P] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R P _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R P _inst_1 _inst_3 _inst_5] {N : Submodule.{u3, u1} R M _inst_1 _inst_2 _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M P (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M P _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M P _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (Submodule.Fg.{u3, u1} R M _inst_1 _inst_2 _inst_4 N)
+Case conversion may be inaccurate. Consider using '#align fg_of_injective fg_of_injectiveₓ'. -/
 theorem fg_of_injective [IsNoetherian R P] {N : Submodule R M} (f : M →ₗ[R] P)
     (hf : Function.Injective f) : N.Fg :=
   @IsNoetherian.noetherian _ _ _ (isNoetherian_of_injective f hf) N
@@ -164,13 +228,21 @@ variable [Semiring R] [AddCommMonoid M] [AddCommMonoid N] [Module R M] [Module R
 
 variable (R M)
 
+#print Module.IsNoetherian.finite /-
 -- see Note [lower instance priority]
 instance (priority := 100) IsNoetherian.finite [IsNoetherian R M] : Finite R M :=
   ⟨IsNoetherian.noetherian ⊤⟩
 #align module.is_noetherian.finite Module.IsNoetherian.finite
+-/
 
 variable {R M}
 
+/- warning: module.finite.of_injective -> Module.Finite.of_injective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : AddCommMonoid.{u3} N] [_inst_4 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_5 : Module.{u1, u3} R N _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u1, u3} R N _inst_1 _inst_3 _inst_5] (f : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u2, succ u3} M N (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5) (fun (_x : LinearMap.{u1, u1, u2, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5) => M -> N) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} R R M N _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) f)) -> (Module.Finite.{u1, u2} R M _inst_1 _inst_2 _inst_4)
+but is expected to have type
+  forall {R : Type.{u3}} {M : Type.{u1}} {N : Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : AddCommMonoid.{u2} N] [_inst_4 : Module.{u3, u1} R M _inst_1 _inst_2] [_inst_5 : Module.{u3, u2} R N _inst_1 _inst_3] [_inst_6 : IsNoetherian.{u3, u2} R N _inst_1 _inst_3 _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5), (Function.Injective.{succ u1, succ u2} M N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (LinearMap.{u3, u3, u1, u2} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) M N _inst_2 _inst_3 _inst_4 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u1, u2} R R M N _inst_1 _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) f)) -> (Module.Finite.{u3, u1} R M _inst_1 _inst_2 _inst_4)
+Case conversion may be inaccurate. Consider using '#align module.finite.of_injective Module.Finite.of_injectiveₓ'. -/
 theorem Finite.of_injective [IsNoetherian R N] (f : M →ₗ[R] N) (hf : Function.Injective f) :
     Finite R M :=
   ⟨fg_of_injective f hf⟩
@@ -190,16 +262,34 @@ open IsNoetherian
 
 include R
 
+/- warning: is_noetherian_of_ker_bot -> isNoetherian_of_ker_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_6 : IsNoetherian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5] (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5), (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) -> (IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4)
+but is expected to have type
+  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : Module.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_6 : IsNoetherian.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_5] (f : LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.ker.{u3, u3, u1, u2, max u1 u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u1, u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)))) f) (Bot.bot.{u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instBotSubmodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) -> (IsNoetherian.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4)
+Case conversion may be inaccurate. Consider using '#align is_noetherian_of_ker_bot isNoetherian_of_ker_botₓ'. -/
 theorem isNoetherian_of_ker_bot [IsNoetherian R P] (f : M →ₗ[R] P) (hf : f.ker = ⊥) :
     IsNoetherian R M :=
   isNoetherian_of_linearEquiv (LinearEquiv.ofInjective f <| LinearMap.ker_eq_bot.mp hf).symm
 #align is_noetherian_of_ker_bot isNoetherian_of_ker_bot
 
+/- warning: fg_of_ker_bot -> fg_of_ker_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_6 : IsNoetherian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5] {N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4} (f : LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5), (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (LinearMap.ker.{u1, u1, u2, u3, max u2 u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R M P (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4))) -> (Submodule.Fg.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4 N)
+but is expected to have type
+  forall {R : Type.{u3}} {M : Type.{u1}} {P : Type.{u2}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : AddCommGroup.{u2} P] [_inst_4 : Module.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_5 : Module.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3)] [_inst_6 : IsNoetherian.{u3, u2} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_5] {N : Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4} (f : LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5), (Eq.{succ u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (LinearMap.ker.{u3, u3, u1, u2, max u1 u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (LinearMap.{u3, u3, u1, u2} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M P (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u1, u2} R R M P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} P _inst_3) _inst_4 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)))) f) (Bot.bot.{u1} (Submodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4) (Submodule.instBotSubmodule.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4))) -> (Submodule.Fg.{u3, u1} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_4 N)
+Case conversion may be inaccurate. Consider using '#align fg_of_ker_bot fg_of_ker_botₓ'. -/
 theorem fg_of_ker_bot [IsNoetherian R P] {N : Submodule R M} (f : M →ₗ[R] P) (hf : f.ker = ⊥) :
     N.Fg :=
   @IsNoetherian.noetherian _ _ _ (isNoetherian_of_ker_bot f hf) N
 #align fg_of_ker_bot fg_of_ker_bot
 
+/- warning: is_noetherian_prod -> isNoetherian_prod is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_6 : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4] [_inst_7 : IsNoetherian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5], IsNoetherian.{u1, max u2 u3} R (Prod.{u2, u3} M P) (Ring.toSemiring.{u1} R _inst_1) (Prod.addCommMonoid.{u2, u3} M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)) (Prod.module.{u1, u2, u3} R M P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : AddCommGroup.{u3} P] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_5 : Module.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)] [_inst_6 : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_4] [_inst_7 : IsNoetherian.{u1, u3} R P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_5], IsNoetherian.{u1, max u3 u2} R (Prod.{u2, u3} M P) (Ring.toSemiring.{u1} R _inst_1) (Prod.instAddCommMonoidSum.{u2, u3} M P (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3)) (Prod.module.{u1, u2, u3} R M P (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} P _inst_3) _inst_4 _inst_5)
+Case conversion may be inaccurate. Consider using '#align is_noetherian_prod isNoetherian_prodₓ'. -/
 instance isNoetherian_prod [IsNoetherian R M] [IsNoetherian R P] : IsNoetherian R (M × P) :=
   ⟨fun s =>
     Submodule.fg_of_fg_map_of_fg_inf_ker (LinearMap.snd R M P) (noetherian _) <|
@@ -208,6 +298,7 @@ instance isNoetherian_prod [IsNoetherian R M] [IsNoetherian R P] : IsNoetherian
       Submodule.map_comap_eq_self this ▸ (noetherian _).map _⟩
 #align is_noetherian_prod isNoetherian_prod
 
+#print isNoetherian_pi /-
 instance isNoetherian_pi {R ι : Type _} {M : ι → Type _} [Ring R] [∀ i, AddCommGroup (M i)]
     [∀ i, Module R (M i)] [Finite ι] [∀ i, IsNoetherian R (M i)] : IsNoetherian R (∀ i, M i) :=
   by
@@ -275,7 +366,9 @@ instance isNoetherian_pi {R ι : Type _} {M : ι → Type _} [Ring R] [∀ i, Ad
         exact has h
       simp only [Or.by_cases, dif_neg this, dif_pos h]
 #align is_noetherian_pi isNoetherian_pi
+-/
 
+#print isNoetherian_pi' /-
 /-- A version of `is_noetherian_pi` for non-dependent functions. We need this instance because
 sometimes Lean fails to apply the dependent version in non-dependent settings (e.g., it fails to
 prove that `ι → ℝ` is finite dimensional over `ℝ`). -/
@@ -283,6 +376,7 @@ instance isNoetherian_pi' {R ι M : Type _} [Ring R] [AddCommGroup M] [Module R
     [IsNoetherian R M] : IsNoetherian R (ι → M) :=
   isNoetherian_pi
 #align is_noetherian_pi' isNoetherian_pi'
+-/
 
 end
 
@@ -295,6 +389,12 @@ universe w
 variable {R M P : Type _} {N : Type w} [Semiring R] [AddCommMonoid M] [Module R M] [AddCommMonoid N]
   [Module R N] [AddCommMonoid P] [Module R P]
 
+/- warning: is_noetherian_iff_well_founded -> isNoetherian_iff_wellFounded is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (GT.gt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3)))))))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2248 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (x._@.Mathlib.RingTheory.Noetherian._hyg.2250 : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => GT.gt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) x._@.Mathlib.RingTheory.Noetherian._hyg.2248 x._@.Mathlib.RingTheory.Noetherian._hyg.2250))
+Case conversion may be inaccurate. Consider using '#align is_noetherian_iff_well_founded isNoetherian_iff_wellFoundedₓ'. -/
 theorem isNoetherian_iff_wellFounded :
     IsNoetherian R M ↔ WellFounded ((· > ·) : Submodule R M → Submodule R M → Prop) :=
   by
@@ -304,6 +404,12 @@ theorem isNoetherian_iff_wellFounded :
       ⟨fun k => (fg_iff_compact k).mpr (h k)⟩⟩
 #align is_noetherian_iff_well_founded isNoetherian_iff_wellFounded
 
+/- warning: is_noetherian_iff_fg_well_founded -> isNoetherian_iff_fg_wellFounded is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_3 N)) (GT.gt.{u2} (Subtype.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_3 N)) (Subtype.hasLt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (fun (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u1, u2} R M _inst_1 _inst_2 _inst_3 N))))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2], Iff (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3) (WellFounded.{succ u1} (Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2457 : Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (x._@.Mathlib.RingTheory.Noetherian._hyg.2459 : Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) => GT.gt.{u1} (Subtype.{succ u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) (Subtype.lt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) (fun (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) => Submodule.Fg.{u2, u1} R M _inst_1 _inst_2 _inst_3 N)) x._@.Mathlib.RingTheory.Noetherian._hyg.2457 x._@.Mathlib.RingTheory.Noetherian._hyg.2459))
+Case conversion may be inaccurate. Consider using '#align is_noetherian_iff_fg_well_founded isNoetherian_iff_fg_wellFoundedₓ'. -/
 theorem isNoetherian_iff_fg_wellFounded :
     IsNoetherian R M ↔
       WellFounded
@@ -337,6 +443,12 @@ theorem isNoetherian_iff_fg_wellFounded :
 
 variable (R M)
 
+/- warning: well_founded_submodule_gt -> wellFounded_submodule_gt is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_8 : Semiring.{u1} R] [_inst_9 : AddCommMonoid.{u2} M] [_inst_10 : Module.{u1, u2} R M _inst_8 _inst_9] [_inst_11 : IsNoetherian.{u1, u2} R M _inst_8 _inst_9 _inst_10], WellFounded.{succ u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (GT.gt.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_8 _inst_9 _inst_10) (Submodule.completeLattice.{u1, u2} R M _inst_8 _inst_9 _inst_10))))))
+but is expected to have type
+  forall (R : Type.{u2}) (M : Type.{u1}) [_inst_8 : Semiring.{u2} R] [_inst_9 : AddCommMonoid.{u1} M] [_inst_10 : Module.{u2, u1} R M _inst_8 _inst_9] [_inst_11 : IsNoetherian.{u2, u1} R M _inst_8 _inst_9 _inst_10], WellFounded.{succ u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (fun (x._@.Mathlib.RingTheory.Noetherian._hyg.2938 : Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (x._@.Mathlib.RingTheory.Noetherian._hyg.2940 : Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) => GT.gt.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_8 _inst_9 _inst_10) (Submodule.completeLattice.{u2, u1} R M _inst_8 _inst_9 _inst_10))))) x._@.Mathlib.RingTheory.Noetherian._hyg.2938 x._@.Mathlib.RingTheory.Noetherian._hyg.2940)
+Case conversion may be inaccurate. Consider using '#align well_founded_submodule_gt wellFounded_submodule_gtₓ'. -/
 theorem wellFounded_submodule_gt (R M) [Semiring R] [AddCommMonoid M] [Module R M] :
     ∀ [IsNoetherian R M], WellFounded ((· > ·) : Submodule R M → Submodule R M → Prop) :=
   isNoetherian_iff_wellFounded.mp
@@ -344,6 +456,12 @@ theorem wellFounded_submodule_gt (R M) [Semiring R] [AddCommMonoid M] [Module R
 
 variable {R M}
 
+/- warning: set_has_maximal_iff_noetherian -> set_has_maximal_iff_noetherian is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (forall (a : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) a) -> (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (M' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => Exists.{0} (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) (fun (H : Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) => forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (Membership.Mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.hasMem.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) I a) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) M' I) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) I M'))))) (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Iff (forall (a : Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)), (Set.Nonempty.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) a) -> (Exists.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (fun (M' : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) => And (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M' a) (forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (Membership.mem.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Set.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Set.instMembershipSet.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3)) I a) -> (LE.le.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) M' I) -> (Eq.{succ u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) I M'))))) (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3)
+Case conversion may be inaccurate. Consider using '#align set_has_maximal_iff_noetherian set_has_maximal_iff_noetherianₓ'. -/
 /-- A module is Noetherian iff every nonempty set of submodules has a maximal submodule among them.
 -/
 theorem set_has_maximal_iff_noetherian :
@@ -352,12 +470,20 @@ theorem set_has_maximal_iff_noetherian :
   by rw [isNoetherian_iff_wellFounded, WellFounded.wellFounded_iff_has_max']
 #align set_has_maximal_iff_noetherian set_has_maximal_iff_noetherian
 
+#print monotone_stabilizes_iff_noetherian /-
 /-- A module is Noetherian iff every increasing chain of submodules stabilizes. -/
 theorem monotone_stabilizes_iff_noetherian :
     (∀ f : ℕ →o Submodule R M, ∃ n, ∀ m, n ≤ m → f n = f m) ↔ IsNoetherian R M := by
   rw [isNoetherian_iff_wellFounded, WellFounded.monotone_chain_condition]
 #align monotone_stabilizes_iff_noetherian monotone_stabilizes_iff_noetherian
+-/
 
+/- warning: is_noetherian.induction -> IsNoetherian.induction is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_8 : IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3] {P : (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) -> Prop}, (forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (forall (J : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (GT.gt.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) J I) -> (P J)) -> (P I)) -> (forall (I : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), P I)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] [_inst_8 : IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3] {P : (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) -> Prop}, (forall (I : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), (forall (J : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), (GT.gt.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Preorder.toLT.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (Submodule.completeLattice.{u2, u1} R M _inst_1 _inst_2 _inst_3))))) J I) -> (P J)) -> (P I)) -> (forall (I : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), P I)
+Case conversion may be inaccurate. Consider using '#align is_noetherian.induction IsNoetherian.inductionₓ'. -/
 /-- If `∀ I > J, P I` implies `P J`, then `P` holds for all submodules. -/
 theorem IsNoetherian.induction [IsNoetherian R M] {P : Submodule R M → Prop}
     (hgt : ∀ I, (∀ J > I, P J) → P I) (I : Submodule R M) : P I :=
@@ -373,6 +499,12 @@ universe w
 variable {R M P : Type _} {N : Type w} [Ring R] [AddCommGroup M] [Module R M] [AddCommGroup N]
   [Module R N] [AddCommGroup P] [Module R P]
 
+/- warning: finite_of_linear_independent -> finite_of_linearIndependent is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : Nontrivial.{u1} R] [_inst_9 : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] {s : Set.{u2} M}, (LinearIndependent.{u2, u1, u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) R M ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} M) Type.{u2} (Set.hasCoeToSort.{u2} M) s) M (coeSubtype.{succ u2} M (fun (x : M) => Membership.Mem.{u2, u2} M (Set.{u2} M) (Set.hasMem.{u2} M) x s)))))) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> (Set.Finite.{u2} M s)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : Nontrivial.{u2} R] [_inst_9 : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] {s : Set.{u1} M}, (LinearIndependent.{u1, u2, u1} (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x s)) R M (Subtype.val.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) x s)) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) -> (Set.Finite.{u1} M s)
+Case conversion may be inaccurate. Consider using '#align finite_of_linear_independent finite_of_linearIndependentₓ'. -/
 theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M}
     (hs : LinearIndependent R (coe : s → M)) : s.Finite :=
   by
@@ -396,6 +528,12 @@ theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M
       by dsimp [GT.gt] <;> simp only [lt_iff_le_not_le, (this _ _).symm] <;> tauto⟩
 #align finite_of_linear_independent finite_of_linearIndependent
 
+/- warning: is_noetherian_of_range_eq_ker -> isNoetherian_of_range_eq_ker is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u2}} {M : Type.{u3}} {P : Type.{u4}} {N : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_6 : AddCommGroup.{u4} P] [_inst_7 : Module.{u2, u4} R P (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6)] [_inst_8 : IsNoetherian.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3] [_inst_9 : IsNoetherian.{u2, u4} R P (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_7] (f : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (g : LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7), (Function.Injective.{succ u3, succ u1} M N (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (fun (_x : LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) => M -> N) (LinearMap.hasCoeToFun.{u2, u2, u3, u1} R R M N (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Surjective.{succ u1, succ u4} N P (coeFn.{max (succ u1) (succ u4), max (succ u1) (succ u4)} (LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7) (fun (_x : LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7) => N -> P) (LinearMap.hasCoeToFun.{u2, u2, u1, u4} R R N P (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) g)) -> (Eq.{succ u1} (Submodule.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5) (LinearMap.range.{u2, u2, u3, u1, max u3 u1} R R M N (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u3, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R M N (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) f) (LinearMap.ker.{u2, u2, u1, u4, max u1 u4} R R N P (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u4} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7) (LinearMap.semilinearMapClass.{u2, u2, u1, u4} R R N P (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u4} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) g)) -> (IsNoetherian.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_5)
+but is expected to have type
+  forall {R : Type.{u3}} {M : Type.{u2}} {P : Type.{u1}} {N : Type.{u4}} [_inst_1 : Ring.{u3} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : AddCommGroup.{u4} N] [_inst_5 : Module.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4)] [_inst_6 : AddCommGroup.{u1} P] [_inst_7 : Module.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6)] [_inst_8 : IsNoetherian.{u3, u2} R M (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] [_inst_9 : IsNoetherian.{u3, u1} R P (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_7] (f : LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (g : LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7), (Function.Injective.{succ u2, succ u4} M N (FunLike.coe.{max (succ u4) (succ u2), succ u2, succ u4} (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => N) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)))) f)) -> (Function.Surjective.{succ u4, succ u1} N P (FunLike.coe.{max (succ u4) (succ u1), succ u4, succ u1} (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)))) g)) -> (Eq.{succ u4} (Submodule.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5) (LinearMap.range.{u3, u3, u2, u4, max u4 u2} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (LinearMap.{u3, u3, u2, u4} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u4} R R M N (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_3 _inst_5 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)))) (RingHomSurjective.ids.{u3} R (Ring.toSemiring.{u3} R _inst_1)) f) (LinearMap.ker.{u3, u3, u4, u1, max u4 u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) (LinearMap.{u3, u3, u4, u1} R R (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1))) N P (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u4, u1} R R N P (Ring.toSemiring.{u3} R _inst_1) (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} P _inst_6) _inst_5 _inst_7 (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R _inst_1)))) g)) -> (IsNoetherian.{u3, u4} R N (Ring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} N _inst_4) _inst_5)
+Case conversion may be inaccurate. Consider using '#align is_noetherian_of_range_eq_ker isNoetherian_of_range_eq_kerₓ'. -/
 /-- If the first and final modules in a short exact sequence are noetherian,
   then the middle module is also noetherian. -/
 theorem isNoetherian_of_range_eq_ker [IsNoetherian R M] [IsNoetherian R P] (f : M →ₗ[R] N)
@@ -408,6 +546,12 @@ theorem isNoetherian_of_range_eq_ker [IsNoetherian R M] [IsNoetherian R P] (f :
       (by simp [Submodule.map_comap_eq, inf_comm]) (by simp [Submodule.comap_map_eq, h])
 #align is_noetherian_of_range_eq_ker isNoetherian_of_range_eq_ker
 
+/- warning: is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot -> IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [I : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), Exists.{1} Nat (fun (n : Nat) => And (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Inf.inf.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f n)) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) f n))) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [I : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), Exists.{1} Nat (fun (n : Nat) => And (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Inf.inf.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instInfSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (LinearMap.ker.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f n)) (LinearMap.range.{u2, u2, u1, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) (RingHomSurjective.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (HPow.hPow.{u1, 0, u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (instHPow.{u1, 0} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) Nat (Monoid.Pow.{u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Module.End.monoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) f n))) (Bot.bot.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))
+Case conversion may be inaccurate. Consider using '#align is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_botₓ'. -/
 /-- For any endomorphism of a Noetherian module, there is some nontrivial iterate
 with disjoint kernel and range.
 -/
@@ -430,6 +574,12 @@ theorem IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot [I : IsNoe
   ring
 #align is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot
 
+/- warning: is_noetherian.injective_of_surjective_endomorphism -> IsNoetherian.injective_of_surjective_endomorphism is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Injective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Injective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
+Case conversion may be inaccurate. Consider using '#align is_noetherian.injective_of_surjective_endomorphism IsNoetherian.injective_of_surjective_endomorphismₓ'. -/
 /-- Any surjective endomorphism of a Noetherian module is injective. -/
 theorem IsNoetherian.injective_of_surjective_endomorphism [IsNoetherian R M] (f : M →ₗ[R] M)
     (s : Surjective f) : Injective f :=
@@ -440,12 +590,24 @@ theorem IsNoetherian.injective_of_surjective_endomorphism [IsNoetherian R M] (f
   exact LinearMap.injective_of_iterate_injective Ne w
 #align is_noetherian.injective_of_surjective_endomorphism IsNoetherian.injective_of_surjective_endomorphism
 
+/- warning: is_noetherian.bijective_of_surjective_endomorphism -> IsNoetherian.bijective_of_surjective_endomorphism is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_8 : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f)) -> (Function.Bijective.{succ u2, succ u2} M M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) f))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_8 : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3), (Function.Surjective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (Function.Bijective.{succ u1, succ u1} M M (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} R R M M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f))
+Case conversion may be inaccurate. Consider using '#align is_noetherian.bijective_of_surjective_endomorphism IsNoetherian.bijective_of_surjective_endomorphismₓ'. -/
 /-- Any surjective endomorphism of a Noetherian module is bijective. -/
 theorem IsNoetherian.bijective_of_surjective_endomorphism [IsNoetherian R M] (f : M →ₗ[R] M)
     (s : Surjective f) : Bijective f :=
   ⟨IsNoetherian.injective_of_surjective_endomorphism f s, s⟩
 #align is_noetherian.bijective_of_surjective_endomorphism IsNoetherian.bijective_of_surjective_endomorphism
 
+/- warning: is_noetherian.disjoint_partial_sups_eventually_bot -> IsNoetherian.disjoint_partialSups_eventually_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [I : IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] (f : Nat -> (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)), (forall (n : Nat), Disjoint.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) (Submodule.orderBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (coeFn.{succ u2, succ u2} (OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))))) (fun (_x : OrderHom.{0, u2} Nat (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))))) => Nat -> (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (OrderHom.hasCoeToFun.{0, u2} Nat (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (SemilatticeSup.toPartialOrder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))))))) (partialSups.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))) f) n) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) -> (Exists.{1} Nat (fun (n : Nat) => forall (m : Nat), (LE.le.{0} Nat Nat.hasLe n m) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (f m) (Bot.bot.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasBot.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [I : IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3] (f : Nat -> (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)), (forall (n : Nat), Disjoint.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (OrderHom.toFun.{0, u1} Nat (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SemilatticeSup.toPartialOrder.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))) (partialSups.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.completeLattice.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) f) n) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) -> (Exists.{1} Nat (fun (n : Nat) => forall (m : Nat), (LE.le.{0} Nat instLENat n m) -> (Eq.{succ u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (f m) (Bot.bot.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))
+Case conversion may be inaccurate. Consider using '#align is_noetherian.disjoint_partial_sups_eventually_bot IsNoetherian.disjoint_partialSups_eventually_botₓ'. -/
 /-- A sequence `f` of submodules of a noetherian module,
 with `f (n+1)` disjoint from the supremum of `f 0`, ..., `f n`,
 is eventually zero.
@@ -468,6 +630,12 @@ theorem IsNoetherian.disjoint_partialSups_eventually_bot [I : IsNoetherian R M]
       (h m).eq_bot_of_ge <| sup_eq_left.1 <| (w (m + 1) <| le_add_right p).symm.trans <| w m p⟩
 #align is_noetherian.disjoint_partial_sups_eventually_bot IsNoetherian.disjoint_partialSups_eventually_bot
 
+/- warning: is_noetherian.equiv_punit_of_prod_injective -> IsNoetherian.equivPunitOfProdInjective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_8 : IsNoetherian.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, max u3 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3), (Function.Injective.{max (succ u3) (succ u1), succ u3} (Prod.{u3, u1} M N) M (coeFn.{max (succ (max u3 u1)) (succ u3), max (succ (max u3 u1)) (succ u3)} (LinearMap.{u2, u2, max u3 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3) (fun (_x : LinearMap.{u2, u2, max u3 u1, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3) => (Prod.{u3, u1} M N) -> M) (LinearMap.hasCoeToFun.{u2, u2, max u3 u1, u3} R R (Prod.{u3, u1} M N) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Prod.addCommMonoid.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (IsNoetherian.equivPunitOfProdInjective._proof_1.{u2} R _inst_1) (IsNoetherian.equivPunitOfProdInjective._proof_2.{u2} R _inst_1) N PUnit.{succ u1} (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (AddCommGroup.toAddCommMonoid.{u1} PUnit.{succ u1} PUnit.addCommGroup.{u1}) _inst_5 (PUnit.module.{u2, u1} R (Ring.toSemiring.{u2} R _inst_1)))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u3} M] [_inst_3 : Module.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2)] [_inst_4 : AddCommGroup.{u1} N] [_inst_5 : Module.{u2, u1} R N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)] [_inst_8 : IsNoetherian.{u2, u3} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) _inst_3] (f : LinearMap.{u2, u2, max u1 u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3), (Function.Injective.{max (succ u1) (succ u3), succ u3} (Prod.{u3, u1} M N) M (FunLike.coe.{max (succ u1) (succ u3), max (succ u1) (succ u3), succ u3} (LinearMap.{u2, u2, max u1 u3, u3} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (Prod.{u3, u1} M N) M (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3) (Prod.{u3, u1} M N) (fun (_x : Prod.{u3, u1} M N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Prod.{u3, u1} M N) => M) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, max u1 u3, u3} R R (Prod.{u3, u1} M N) M (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (Prod.instAddCommMonoidSum.{u3, u1} M N (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (Prod.module.{u2, u3, u1} R M N (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) _inst_3 _inst_5) _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)))) f)) -> (LinearEquiv.{u2, u2, u1, u1} R R (Ring.toSemiring.{u2} R _inst_1) (Ring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (Ring.toSemiring.{u2} R _inst_1)) N PUnit.{succ u1} (AddCommGroup.toAddCommMonoid.{u1} N _inst_4) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} PUnit.{succ u1} (LinearOrderedCancelAddCommMonoid.toOrderedCancelAddCommMonoid.{u1} PUnit.{succ u1} PUnit.linearOrderedCancelAddCommMonoid.{u1})) _inst_5 (PUnit.module.{u2, u1} R (Ring.toSemiring.{u2} R _inst_1)))
+Case conversion may be inaccurate. Consider using '#align is_noetherian.equiv_punit_of_prod_injective IsNoetherian.equivPunitOfProdInjectiveₓ'. -/
 /-- If `M ⊕ N` embeds into `M`, for `M` noetherian over `R`, then `N` is trivial.
 -/
 noncomputable def IsNoetherian.equivPunitOfProdInjective [IsNoetherian R M] (f : M × N →ₗ[R] M)
@@ -485,6 +653,7 @@ noncomputable def IsNoetherian.equivPunitOfProdInjective [IsNoetherian R M] (f :
 
 end
 
+#print IsNoetherianRing /-
 /-- A (semi)ring is Noetherian if it is Noetherian as a module over itself,
 i.e. all its ideals are finitely generated.
 -/
@@ -492,23 +661,31 @@ i.e. all its ideals are finitely generated.
 def IsNoetherianRing (R) [Semiring R] :=
   IsNoetherian R R
 #align is_noetherian_ring IsNoetherianRing
+-/
 
+#print isNoetherianRing_iff /-
 theorem isNoetherianRing_iff {R} [Semiring R] : IsNoetherianRing R ↔ IsNoetherian R R :=
   Iff.rfl
 #align is_noetherian_ring_iff isNoetherianRing_iff
+-/
 
+#print isNoetherianRing_iff_ideal_fg /-
 /-- A ring is Noetherian if and only if all its ideals are finitely-generated. -/
 theorem isNoetherianRing_iff_ideal_fg (R : Type _) [Semiring R] :
     IsNoetherianRing R ↔ ∀ I : Ideal R, I.Fg :=
   isNoetherianRing_iff.trans isNoetherian_def
 #align is_noetherian_ring_iff_ideal_fg isNoetherianRing_iff_ideal_fg
+-/
 
+#print isNoetherian_of_finite /-
 -- see Note [lower instance priority]
 instance (priority := 80) isNoetherian_of_finite (R M) [Finite M] [Semiring R] [AddCommMonoid M]
     [Module R M] : IsNoetherian R M :=
   ⟨fun s => ⟨(s : Set M).toFinite.toFinset, by rw [Set.Finite.coe_toFinset, Submodule.span_eq]⟩⟩
 #align is_noetherian_of_finite isNoetherian_of_finite
+-/
 
+#print isNoetherian_of_subsingleton /-
 -- see Note [lower instance priority]
 /-- Modules over the trivial ring are Noetherian. -/
 instance (priority := 100) isNoetherian_of_subsingleton (R M) [Subsingleton R] [Semiring R]
@@ -516,7 +693,14 @@ instance (priority := 100) isNoetherian_of_subsingleton (R M) [Subsingleton R] [
   haveI := Module.subsingleton R M
   isNoetherian_of_finite R M
 #align is_noetherian_of_subsingleton isNoetherian_of_subsingleton
+-/
 
+/- warning: is_noetherian_of_submodule_of_noetherian -> isNoetherian_of_submodule_of_noetherian is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] (N : Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3), (IsNoetherian.{u1, u2} R M _inst_1 _inst_2 _inst_3) -> (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u1, u2} R M _inst_1 _inst_2 _inst_3)) N) _inst_1 (Submodule.addCommMonoid.{u1, u2} R M _inst_1 _inst_2 _inst_3 N) (Submodule.module.{u1, u2} R M _inst_1 _inst_2 _inst_3 N))
+but is expected to have type
+  forall (R : Type.{u2}) (M : Type.{u1}) [_inst_1 : Semiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M _inst_1 _inst_2] (N : Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3), (IsNoetherian.{u2, u1} R M _inst_1 _inst_2 _inst_3) -> (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M _inst_1 _inst_2 _inst_3) M (Submodule.setLike.{u2, u1} R M _inst_1 _inst_2 _inst_3)) x N)) _inst_1 (Submodule.addCommMonoid.{u2, u1} R M _inst_1 _inst_2 _inst_3 N) (Submodule.module.{u2, u1} R M _inst_1 _inst_2 _inst_3 N))
+Case conversion may be inaccurate. Consider using '#align is_noetherian_of_submodule_of_noetherian isNoetherian_of_submodule_of_noetherianₓ'. -/
 theorem isNoetherian_of_submodule_of_noetherian (R M) [Semiring R] [AddCommMonoid M] [Module R M]
     (N : Submodule R M) (h : IsNoetherian R M) : IsNoetherian R N :=
   by
@@ -524,13 +708,21 @@ theorem isNoetherian_of_submodule_of_noetherian (R M) [Semiring R] [AddCommMonoi
   exact OrderEmbedding.wellFounded (Submodule.MapSubtype.orderEmbedding N).dual h
 #align is_noetherian_of_submodule_of_noetherian isNoetherian_of_submodule_of_noetherian
 
+#print Submodule.Quotient.isNoetherian /-
 instance Submodule.Quotient.isNoetherian {R} [Ring R] {M} [AddCommGroup M] [Module R M]
     (N : Submodule R M) [h : IsNoetherian R M] : IsNoetherian R (M ⧸ N) :=
   by
   rw [isNoetherian_iff_wellFounded] at h⊢
   exact OrderEmbedding.wellFounded (Submodule.comapMkQOrderEmbedding N).dual h
 #align submodule.quotient.is_noetherian Submodule.Quotient.isNoetherian
+-/
 
+/- warning: is_noetherian_of_tower -> isNoetherian_of_tower is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {S : Type.{u2}} {M : Type.{u3}} [_inst_1 : Semiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} M] [_inst_4 : SMul.{u1, u2} R S] [_inst_5 : Module.{u2, u3} S M _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R M _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S M _inst_4 (SMulZeroClass.toHasSmul.{u2, u3} S M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S M (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S M (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Module.toMulActionWithZero.{u2, u3} S M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_3))) (Module.toMulActionWithZero.{u1, u3} R M _inst_1 _inst_3 _inst_6))))], (IsNoetherian.{u1, u3} R M _inst_1 _inst_3 _inst_6) -> (IsNoetherian.{u2, u3} S M _inst_2 _inst_3 _inst_5)
+but is expected to have type
+  forall (R : Type.{u3}) {S : Type.{u2}} {M : Type.{u1}} [_inst_1 : Semiring.{u3} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : SMul.{u3, u2} R S] [_inst_5 : Module.{u2, u1} S M _inst_2 _inst_3] [_inst_6 : Module.{u3, u1} R M _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u3, u2, u1} R S M _inst_4 (SMulZeroClass.toSMul.{u2, u1} S M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u1} S M (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u1} S M (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u2, u1} S M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M (Semiring.toMonoidWithZero.{u3} R _inst_1) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u3, u1} R M _inst_1 _inst_3 _inst_6))))], (IsNoetherian.{u3, u1} R M _inst_1 _inst_3 _inst_6) -> (IsNoetherian.{u2, u1} S M _inst_2 _inst_3 _inst_5)
+Case conversion may be inaccurate. Consider using '#align is_noetherian_of_tower isNoetherian_of_towerₓ'. -/
 /-- If `M / S / R` is a scalar tower, and `M / R` is Noetherian, then `M / S` is
 also noetherian. -/
 theorem isNoetherian_of_tower (R) {S M} [Semiring R] [Semiring S] [AddCommMonoid M] [SMul R S]
@@ -540,6 +732,12 @@ theorem isNoetherian_of_tower (R) {S M} [Semiring R] [Semiring S] [AddCommMonoid
   refine' (Submodule.restrictScalarsEmbedding R S M).dual.WellFounded h
 #align is_noetherian_of_tower isNoetherian_of_tower
 
+/- warning: is_noetherian_of_fg_of_noetherian -> isNoetherian_of_fg_of_noetherian is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] (N : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_4 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], (Submodule.Fg.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 N) -> (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) N) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 N) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 N))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] (N : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) [_inst_4 : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], (Submodule.Fg.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 N) -> (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x N)) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 N) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 N))
+Case conversion may be inaccurate. Consider using '#align is_noetherian_of_fg_of_noetherian isNoetherian_of_fg_of_noetherianₓ'. -/
 theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module R M]
     (N : Submodule R M) [IsNoetherianRing R] (hN : N.Fg) : IsNoetherian R N :=
   by
@@ -574,12 +772,24 @@ theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module
   rw [Finsupp.not_mem_support_iff.1 hx, zero_smul]
 #align is_noetherian_of_fg_of_noetherian isNoetherian_of_fg_of_noetherian
 
+/- warning: is_noetherian_of_fg_of_noetherian' -> isNoetherian_of_fg_of_noetherian' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], (Submodule.Fg.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) -> (IsNoetherian.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], (Submodule.Fg.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Top.top.{u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))) -> (IsNoetherian.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)
+Case conversion may be inaccurate. Consider using '#align is_noetherian_of_fg_of_noetherian' isNoetherian_of_fg_of_noetherian'ₓ'. -/
 theorem isNoetherian_of_fg_of_noetherian' {R M} [Ring R] [AddCommGroup M] [Module R M]
     [IsNoetherianRing R] (h : (⊤ : Submodule R M).Fg) : IsNoetherian R M :=
   have : IsNoetherian R (⊤ : Submodule R M) := isNoetherian_of_fg_of_noetherian _ h
   isNoetherian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl)
 #align is_noetherian_of_fg_of_noetherian' isNoetherian_of_fg_of_noetherian'
 
+/- warning: is_noetherian_span_of_finite -> isNoetherian_span_of_finite is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)] {A : Set.{u2} M}, (Set.Finite.{u2} M A) -> (IsNoetherian.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 A)) (Ring.toSemiring.{u1} R _inst_1) (Submodule.addCommMonoid.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 A)) (Submodule.module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 (Submodule.span.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 A)))
+but is expected to have type
+  forall (R : Type.{u2}) {M : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] [_inst_4 : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)] {A : Set.{u1} M}, (Set.Finite.{u1} M A) -> (IsNoetherian.{u2, u1} R (Subtype.{succ u1} M (fun (x : M) => Membership.mem.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) M (Submodule.setLike.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)) x (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 A))) (Ring.toSemiring.{u2} R _inst_1) (Submodule.addCommMonoid.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 A)) (Submodule.module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 (Submodule.span.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_1) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 A)))
+Case conversion may be inaccurate. Consider using '#align is_noetherian_span_of_finite isNoetherian_span_of_finiteₓ'. -/
 /-- In a module over a noetherian ring, the submodule generated by finitely many vectors is
 noetherian. -/
 theorem isNoetherian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R M]
@@ -587,6 +797,12 @@ theorem isNoetherian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R
   isNoetherian_of_fg_of_noetherian _ (Submodule.fg_def.mpr ⟨A, hA, rfl⟩)
 #align is_noetherian_span_of_finite isNoetherian_span_of_finite
 
+/- warning: is_noetherian_ring_of_surjective -> isNoetherianRing_of_surjective is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] (S : Type.{u2}) [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))), (Function.Surjective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) f)) -> (forall [H : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], IsNoetherianRing.{u2} S (Ring.toSemiring.{u2} S _inst_2))
+but is expected to have type
+  forall (R : Type.{u2}) [_inst_1 : Ring.{u2} R] (S : Type.{u1}) [_inst_2 : Ring.{u1} S] (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))), (Function.Surjective.{succ u2, succ u1} R S (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2)))))) f)) -> (forall [H : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], IsNoetherianRing.{u1} S (Ring.toSemiring.{u1} S _inst_2))
+Case conversion may be inaccurate. Consider using '#align is_noetherian_ring_of_surjective isNoetherianRing_of_surjectiveₓ'. -/
 theorem isNoetherianRing_of_surjective (R) [Ring R] (S) [Ring S] (f : R →+* S)
     (hf : Function.Surjective f) [H : IsNoetherianRing R] : IsNoetherianRing S :=
   by
@@ -594,16 +810,34 @@ theorem isNoetherianRing_of_surjective (R) [Ring R] (S) [Ring S] (f : R →+* S)
   exact OrderEmbedding.wellFounded (Ideal.orderEmbeddingOfSurjective f hf).dual H
 #align is_noetherian_ring_of_surjective isNoetherianRing_of_surjective
 
+/- warning: is_noetherian_ring_range -> isNoetherianRing_range is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) [_inst_3 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], IsNoetherianRing.{u2} (coeSort.{succ u2, succ (succ u2)} (Subring.{u2} S _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subring.{u2} S _inst_2) S (Subring.setLike.{u2} S _inst_2)) (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f)) (Ring.toSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (Subring.{u2} S _inst_2) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subring.{u2} S _inst_2) S (Subring.setLike.{u2} S _inst_2)) (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f)) (Subring.toRing.{u2} S _inst_2 (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2))) [_inst_3 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], IsNoetherianRing.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subring.{u2} S _inst_2) (SetLike.instMembership.{u2, u2} (Subring.{u2} S _inst_2) S (Subring.instSetLikeSubring.{u2} S _inst_2)) x (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f))) (Ring.toSemiring.{u2} (Subtype.{succ u2} S (fun (x : S) => Membership.mem.{u2, u2} S (Subring.{u2} S _inst_2) (SetLike.instMembership.{u2, u2} (Subring.{u2} S _inst_2) S (Subring.instSetLikeSubring.{u2} S _inst_2)) x (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f))) (Subring.toRing.{u2} S _inst_2 (RingHom.range.{u1, u2} R S _inst_1 _inst_2 f)))
+Case conversion may be inaccurate. Consider using '#align is_noetherian_ring_range isNoetherianRing_rangeₓ'. -/
 instance isNoetherianRing_range {R} [Ring R] {S} [Ring S] (f : R →+* S) [IsNoetherianRing R] :
     IsNoetherianRing f.range :=
   isNoetherianRing_of_surjective R f.range f.range_restrict f.rangeRestrict_surjective
 #align is_noetherian_ring_range isNoetherianRing_range
 
+/- warning: is_noetherian_ring_of_ring_equiv -> isNoetherianRing_of_ringEquiv is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : Ring.{u1} R] {S : Type.{u2}} [_inst_2 : Ring.{u2} S], (RingEquiv.{u1, u2} R S (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R _inst_1)) (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R _inst_1)) (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S _inst_2)) (Distrib.toHasAdd.{u2} S (Ring.toDistrib.{u2} S _inst_2))) -> (forall [_inst_3 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R _inst_1)], IsNoetherianRing.{u2} S (Ring.toSemiring.{u2} S _inst_2))
+but is expected to have type
+  forall (R : Type.{u2}) [_inst_1 : Ring.{u2} R] {S : Type.{u1}} [_inst_2 : Ring.{u1} S], (RingEquiv.{u2, u1} R S (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))) (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2))) (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1))))) (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S _inst_2)))))) -> (forall [_inst_3 : IsNoetherianRing.{u2} R (Ring.toSemiring.{u2} R _inst_1)], IsNoetherianRing.{u1} S (Ring.toSemiring.{u1} S _inst_2))
+Case conversion may be inaccurate. Consider using '#align is_noetherian_ring_of_ring_equiv isNoetherianRing_of_ringEquivₓ'. -/
 theorem isNoetherianRing_of_ringEquiv (R) [Ring R] {S} [Ring S] (f : R ≃+* S) [IsNoetherianRing R] :
     IsNoetherianRing S :=
   isNoetherianRing_of_surjective R S f.toRingHom f.toEquiv.Surjective
 #align is_noetherian_ring_of_ring_equiv isNoetherianRing_of_ringEquiv
 
+/- warning: is_noetherian_ring.is_nilpotent_nilradical -> IsNoetherianRing.isNilpotent_nilradical is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], IsNilpotent.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MulZeroClass.toHasZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Monoid.Pow.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (nilradical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R] [_inst_2 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], IsNilpotent.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toCommMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemCommSemiring.toCommSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.instIdemCommSemiringIdealToSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Monoid.Pow.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (nilradical.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))
+Case conversion may be inaccurate. Consider using '#align is_noetherian_ring.is_nilpotent_nilradical IsNoetherianRing.isNilpotent_nilradicalₓ'. -/
 theorem IsNoetherianRing.isNilpotent_nilradical (R : Type _) [CommRing R] [IsNoetherianRing R] :
     IsNilpotent (nilradical R) :=
   by

da420a8c

bump to nightly-2023-03-12-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/f24cc2891c0e328f0ee8c57387103aa462c44b5e

5e501a2f

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Kevin Buzzard
 
 ! This file was ported from Lean 3 source module ring_theory.noetherian
-! leanprover-community/mathlib commit 9b2660e1b25419042c8da10bf411aa3c67f14383
+! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -540,11 +540,6 @@ theorem isNoetherian_of_tower (R) {S M} [Semiring R] [Semiring S] [AddCommMonoid
   refine' (Submodule.restrictScalarsEmbedding R S M).dual.WellFounded h
 #align is_noetherian_of_tower isNoetherian_of_tower
 
-instance Ideal.Quotient.isNoetherianRing {R : Type _} [CommRing R] [h : IsNoetherianRing R]
-    (I : Ideal R) : IsNoetherianRing (R ⧸ I) :=
-  isNoetherianRing_iff.mpr <| isNoetherian_of_tower R <| Submodule.Quotient.isNoetherian _
-#align ideal.quotient.is_noetherian_ring Ideal.Quotient.isNoetherianRing
-
 theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module R M]
     (N : Submodule R M) [IsNoetherianRing R] (hN : N.Fg) : IsNoetherian R N :=
   by

9b2660e1

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

210657c4

Chore: Weaken hypotheses for proof that Noetherian is an extension property (#12453)

The middle term of a three term exact sequence with outer terms Noetherian is Noetherian.

33a5bedd

Diff

@@ -119,6 +119,14 @@ theorem isNoetherian_of_surjective (f : M →ₗ[R] P) (hf : LinearMap.range f =
 
 variable {M}
 
+instance isNoetherian_quotient {R} [Ring R] {M} [AddCommGroup M] [Module R M]
+    (N : Submodule R M) [IsNoetherian R M] : IsNoetherian R (M ⧸ N) :=
+  isNoetherian_of_surjective _ _ (LinearMap.range_eq_top.mpr N.mkQ_surjective)
+#align submodule.quotient.is_noetherian isNoetherian_quotient
+
+-- deprecated on 2024-04-27
+@[deprecated, nolint defLemma] alias Submodule.Quotient.isNoetherian := isNoetherian_quotient
+
 theorem isNoetherian_of_linearEquiv (f : M ≃ₗ[R] P) [IsNoetherian R M] : IsNoetherian R P :=
   isNoetherian_of_surjective _ f.toLinearMap f.range
 #align is_noetherian_of_linear_equiv isNoetherian_of_linearEquiv
@@ -404,17 +412,23 @@ theorem LinearIndependent.set_finite_of_isNoetherian [Nontrivial R] {s : Set M}
 alias finite_of_linearIndependent := LinearIndependent.set_finite_of_isNoetherian
 #align finite_of_linear_independent LinearIndependent.set_finite_of_isNoetherian
 
-/-- If the first and final modules in a short exact sequence are Noetherian,
+/-- If the first and final modules in an exact sequence are Noetherian,
   then the middle module is also Noetherian. -/
-theorem isNoetherian_of_range_eq_ker [IsNoetherian R P] (f : M →ₗ[R] N)
-    (g : N →ₗ[R] P) (hf : Function.Injective f) (hg : Function.Surjective g)
-    (h : LinearMap.range f = LinearMap.ker g) :
+theorem isNoetherian_of_range_eq_ker [IsNoetherian R P]
+    (f : M →ₗ[R] N) (g : N →ₗ[R] P) (h : LinearMap.range f = LinearMap.ker g) :
     IsNoetherian R N :=
   isNoetherian_iff_wellFounded.2 <|
-    wellFounded_gt_exact_sequence (wellFounded_submodule_gt R M) (wellFounded_submodule_gt R P)
-      (LinearMap.range f) (Submodule.map f) (Submodule.comap f) (Submodule.comap g)
-      (Submodule.map g) (Submodule.gciMapComap hf) (Submodule.giMapComap hg)
-      (by simp [Submodule.map_comap_eq, inf_comm]) (by simp [Submodule.comap_map_eq, h])
+    wellFounded_gt_exact_sequence
+      (wellFounded_submodule_gt R _) (wellFounded_submodule_gt R _)
+      (LinearMap.range f)
+      (Submodule.map (f.ker.liftQ f <| le_rfl))
+      (Submodule.comap (f.ker.liftQ f <| le_rfl))
+      (Submodule.comap g.rangeRestrict) (Submodule.map g.rangeRestrict)
+      (Submodule.gciMapComap <| LinearMap.ker_eq_bot.mp <|
+        Submodule.ker_liftQ_eq_bot _ _ _ (le_refl _))
+      (Submodule.giMapComap g.surjective_rangeRestrict)
+      (by simp [Submodule.map_comap_eq, inf_comm, Submodule.range_liftQ])
+      (by simp [Submodule.comap_map_eq, h])
 #align is_noetherian_of_range_eq_ker isNoetherian_of_range_eq_ker
 
 /-- For an endomorphism of a Noetherian module, any sufficiently large iterate has disjoint kernel
@@ -534,12 +548,6 @@ theorem isNoetherian_of_submodule_of_noetherian (R M) [Semiring R] [AddCommMonoi
   exact OrderEmbedding.wellFounded (Submodule.MapSubtype.orderEmbedding N).dual h
 #align is_noetherian_of_submodule_of_noetherian isNoetherian_of_submodule_of_noetherian
 
-instance Submodule.Quotient.isNoetherian {R} [Ring R] {M} [AddCommGroup M] [Module R M]
-    (N : Submodule R M) [h : IsNoetherian R M] : IsNoetherian R (M ⧸ N) := by
-  rw [isNoetherian_iff_wellFounded] at h ⊢
-  exact OrderEmbedding.wellFounded (Submodule.comapMkQOrderEmbedding N).dual h
-#align submodule.quotient.is_noetherian Submodule.Quotient.isNoetherian
-
 /-- If `M / S / R` is a scalar tower, and `M / R` is Noetherian, then `M / S` is
 also noetherian. -/
 theorem isNoetherian_of_tower (R) {S M} [Semiring R] [Semiring S] [AddCommMonoid M] [SMul R S]

210657c4

chore: split RingTheory.Nilpotent (#12184)

Mathlib.RingTheory.Nilpotent has a few very simple definitions (Mathlib.Data.Nat.Lattice is sufficient to state them), but needs some pretty heavy imports (ideals, linear algebra) towards the end. This change moves the heavier parts into a new file.

bdfbc7fa

Diff

@@ -5,7 +5,7 @@ Authors: Mario Carneiro, Kevin Buzzard
 -/
 import Mathlib.Order.Filter.EventuallyConst
 import Mathlib.RingTheory.Finiteness
-import Mathlib.RingTheory.Nilpotent
+import Mathlib.RingTheory.Nilpotent.Lemmas
 
 #align_import ring_theory.noetherian from "leanprover-community/mathlib"@"210657c4ea4a4a7b234392f70a3a2a83346dfa90"

210657c4

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -66,9 +66,7 @@ attribute [inherit_doc IsNoetherian] IsNoetherian.noetherian
 section
 
 variable {R : Type*} {M : Type*} {P : Type*}
-
 variable [Semiring R] [AddCommMonoid M] [AddCommMonoid P]
-
 variable [Module R M] [Module R P]
 
 open IsNoetherian
@@ -147,9 +145,7 @@ end
 namespace Module
 
 variable {R M N : Type*}
-
 variable [Semiring R] [AddCommMonoid M] [AddCommMonoid N] [Module R M] [Module R N]
-
 variable (R M)
 
 -- see Note [lower instance priority]
@@ -173,9 +169,7 @@ end Module
 section
 
 variable {R : Type*} {M : Type*} {P : Type*}
-
 variable [Ring R] [AddCommGroup M] [AddCommGroup P]
-
 variable [Module R M] [Module R P]
 
 open IsNoetherian

210657c4

chore: remove terminal, terminal refines (#10762)

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

ea36aa7d

Diff

@@ -551,7 +551,7 @@ also noetherian. -/
 theorem isNoetherian_of_tower (R) {S M} [Semiring R] [Semiring S] [AddCommMonoid M] [SMul R S]
     [Module S M] [Module R M] [IsScalarTower R S M] (h : IsNoetherian R M) : IsNoetherian S M := by
   rw [isNoetherian_iff_wellFounded] at h ⊢
-  refine' (Submodule.restrictScalarsEmbedding R S M).dual.wellFounded h
+  exact (Submodule.restrictScalarsEmbedding R S M).dual.wellFounded h
 #align is_noetherian_of_tower isNoetherian_of_tower
 
 theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module R M]

210657c4

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

a13e8040

Diff

@@ -204,8 +204,8 @@ instance isNoetherian_pi {R ι : Type*} {M : ι → Type*}
     [∀ i, IsNoetherian R (M i)] : IsNoetherian R (∀ i, M i) := by
   cases nonempty_fintype ι
   haveI := Classical.decEq ι
-  suffices on_finset : ∀ s : Finset ι, IsNoetherian R (∀ i : s, M i)
-  · let coe_e := Equiv.subtypeUnivEquiv <| @Finset.mem_univ ι _
+  suffices on_finset : ∀ s : Finset ι, IsNoetherian R (∀ i : s, M i) by
+    let coe_e := Equiv.subtypeUnivEquiv <| @Finset.mem_univ ι _
     letI : IsNoetherian R (∀ i : Finset.univ, M (coe_e i)) := on_finset Finset.univ
     exact isNoetherian_of_linearEquiv (LinearEquiv.piCongrLeft R M coe_e)
   intro s
@@ -472,8 +472,8 @@ theorem IsNoetherian.disjoint_partialSups_eventually_bot
     (f : ℕ → Submodule R M) (h : ∀ n, Disjoint (partialSups f n) (f (n + 1))) :
     ∃ n : ℕ, ∀ m, n ≤ m → f m = ⊥ := by
   -- A little off-by-one cleanup first:
-  suffices t : ∃ n : ℕ, ∀ m, n ≤ m → f (m + 1) = ⊥
-  · obtain ⟨n, w⟩ := t
+  suffices t : ∃ n : ℕ, ∀ m, n ≤ m → f (m + 1) = ⊥ by
+    obtain ⟨n, w⟩ := t
     use n + 1
     rintro (_ | m) p
     · cases p

210657c4

feat: Add Module.Free and Module.Finite instances for ideals (#9804)

Add also a NoZeroSMulDivisors instance.

These instances, in particular, imply directly that integral ideals of number fields are free and finite $\mathbb{Z}$-modules.

ca796bf0

Diff

@@ -157,6 +157,10 @@ instance (priority := 100) IsNoetherian.finite [IsNoetherian R M] : Finite R M :
   ⟨IsNoetherian.noetherian ⊤⟩
 #align module.is_noetherian.finite Module.IsNoetherian.finite
 
+instance {R₁ S : Type*} [CommSemiring R₁] [Semiring S] [Algebra R₁ S]
+    [IsNoetherian R₁ S] (I : Ideal S) : Finite R₁ I :=
+  IsNoetherian.finite R₁ ((I : Submodule S S).restrictScalars R₁)
+
 variable {R M}
 
 theorem Finite.of_injective [IsNoetherian R N] (f : M →ₗ[R] N) (hf : Function.Injective f) :

210657c4

chore(*): replace $ with <| (#9319)

See Zulip thread for the discussion.

9f6d3388

Diff

@@ -589,7 +589,7 @@ instance isNoetherian_of_isNoetherianRing_of_finite (R M : Type*)
     [Ring R] [AddCommGroup M] [Module R M] [IsNoetherianRing R] [Module.Finite R M] :
     IsNoetherian R M :=
   have : IsNoetherian R (⊤ : Submodule R M) :=
-    isNoetherian_of_fg_of_noetherian _ $ Module.finite_def.mp inferInstance
+    isNoetherian_of_fg_of_noetherian _ <| Module.finite_def.mp inferInstance
   isNoetherian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl)
 #align is_noetherian_of_fg_of_noetherian' isNoetherian_of_isNoetherianRing_of_finite

210657c4

chore: deduplicate LinearIndependent.set_finite_of_isNoetherian (#9300)

Also moved several lemmas into Mathlib/LinearAlgebra/Basis.lean.

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

7392ea7c

Diff

@@ -385,28 +385,26 @@ lemma Submodule.finite_ne_bot_of_independent {ι : Type*} {N : ι → Submodule
   CompleteLattice.WellFounded.finite_ne_bot_of_independent
     (isNoetherian_iff_wellFounded.mp inferInstance) h
 
-theorem finite_of_linearIndependent [Nontrivial R] {s : Set M}
-    (hs : LinearIndependent R ((↑) : s → M)) : s.Finite := by
-  refine'
-    by_contradiction fun hf =>
-      (RelEmbedding.wellFounded_iff_no_descending_seq.1 (wellFounded_submodule_gt R M)).elim' _
-  have f : ℕ ↪ s := Set.Infinite.natEmbedding s hf
-  have : ∀ n, (↑) ∘ f '' { m | m ≤ n } ⊆ s := by
-    rintro n x ⟨y, _, rfl⟩
-    exact (f y).2
-  let coe' : s → M := (↑)
-  have : ∀ a b : ℕ, a ≤ b ↔
-    span R (coe' ∘ f '' { m | m ≤ a }) ≤ span R ((↑) ∘ f '' { m | m ≤ b }) := by
-    intro a b
-    rw [span_le_span_iff hs (this a) (this b),
-      Set.image_subset_image_iff (Subtype.coe_injective.comp f.injective), Set.subset_def]
-    exact ⟨fun hab x (hxa : x ≤ a) => le_trans hxa hab, fun hx => hx a (le_refl a)⟩
-  exact
-    ⟨⟨fun n => span R (coe' ∘ f '' { m | m ≤ n }), fun x y => by
-        rw [le_antisymm_iff, (this x y).symm, (this y x).symm, ← le_antisymm_iff, imp_self]
-        trivial⟩,
-      by dsimp [GT.gt]; simp only [lt_iff_le_not_le, (this _ _).symm]; tauto⟩
-#align finite_of_linear_independent finite_of_linearIndependent
+/-- A linearly-independent family of vectors in a module over a non-trivial ring must be finite if
+the module is Noetherian. -/
+theorem LinearIndependent.finite_of_isNoetherian [Nontrivial R] {ι} {v : ι → M}
+    (hv : LinearIndependent R v) : Finite ι := by
+  have hwf := isNoetherian_iff_wellFounded.mp (by infer_instance : IsNoetherian R M)
+  refine' CompleteLattice.WellFounded.finite_of_independent hwf hv.independent_span_singleton
+    fun i contra => _
+  apply hv.ne_zero i
+  have : v i ∈ R ∙ v i := Submodule.mem_span_singleton_self (v i)
+  rwa [contra, Submodule.mem_bot] at this
+#align linear_independent.finite_of_is_noetherian LinearIndependent.finite_of_isNoetherian
+
+theorem LinearIndependent.set_finite_of_isNoetherian [Nontrivial R] {s : Set M}
+    (hi : LinearIndependent R ((↑) : s → M)) : s.Finite :=
+  @Set.toFinite _ _ hi.finite_of_isNoetherian
+#align linear_independent.set_finite_of_is_noetherian LinearIndependent.set_finite_of_isNoetherian
+
+@[deprecated]
+alias finite_of_linearIndependent := LinearIndependent.set_finite_of_isNoetherian
+#align finite_of_linear_independent LinearIndependent.set_finite_of_isNoetherian
 
 /-- If the first and final modules in a short exact sequence are Noetherian,
   then the middle module is also Noetherian. -/

210657c4

chore: reduce imports in Mathlib.RingTheory.Noetherian (#9322)

42060a27

Diff

@@ -3,14 +3,7 @@ Copyright (c) 2018 Mario Carneiro, Kevin Buzzard. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Kevin Buzzard
 -/
-import Mathlib.Algebra.Algebra.Subalgebra.Basic
-import Mathlib.Algebra.Algebra.Tower
-import Mathlib.Algebra.Ring.Idempotents
-import Mathlib.GroupTheory.Finiteness
-import Mathlib.LinearAlgebra.LinearIndependent
-import Mathlib.Order.CompactlyGenerated
 import Mathlib.Order.Filter.EventuallyConst
-import Mathlib.Order.OrderIsoNat
 import Mathlib.RingTheory.Finiteness
 import Mathlib.RingTheory.Nilpotent

210657c4

feat: Better lemmas for transferring finite sums along equivalences (#9237)

Lemmas around this were a mess, throth in terms of names, statement and location. This PR standardises everything to be in Algebra.BigOperators.Basic and changes the lemmas to take in InjOn and SurjOn assumptions where possible (and where impossible make sure the hypotheses are taken in the correct order) and moves the equality of functions hypothesis last.

Also add a few lemmas that help fix downstream uses by golfing.

From LeanAPAP and LeanCamCombi

82c60323

Diff

@@ -588,7 +588,7 @@ theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module
     rcases hn with ⟨l, hl1, hl2⟩
     refine' ⟨fun x => l x, Subtype.ext _⟩
     change (∑ i in s.attach, l i • (i : M)) = n
-    rw [@Finset.sum_attach M M s _ fun i => l i • i, ← hl2,
+    rw [s.sum_attach fun i ↦ l i • i, ← hl2,
       Finsupp.total_apply, Finsupp.sum, eq_comm]
     refine' Finset.sum_subset hl1 fun x _ hx => _
     rw [Finsupp.not_mem_support_iff.1 hx, zero_smul]

210657c4

chore: remove uses of cases' (#9171)

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

3fca282c

Diff

@@ -449,7 +449,7 @@ lemma LinearMap.eventually_iSup_ker_pow_eq (f : M →ₗ[R] M) :
     monotone_stabilizes_iff_noetherian.mpr inferInstance f.iterateKer
   refine eventually_atTop.mpr ⟨n, fun m hm ↦ ?_⟩
   refine le_antisymm (iSup_le fun l ↦ ?_) (le_iSup (fun i ↦ LinearMap.ker (f ^ i)) m)
-  cases' le_or_lt m l with h h
+  rcases le_or_lt m l with h | h
   · rw [← hn _ (hm.trans h), hn _ hm]
   · exact f.iterateKer.monotone h.le

210657c4

feat: make isNoetherian_of_isNoetherianRing_of_finite an instance (#8999)

Make isNoetherian_of_isNoetherianRing_of_finite an instance: this was impossible in Lean 3 because of a loop.

c4988d10

Diff

@@ -594,9 +594,7 @@ theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module
     rw [Finsupp.not_mem_support_iff.1 hx, zero_smul]
 #align is_noetherian_of_fg_of_noetherian isNoetherian_of_fg_of_noetherian
 
--- It would be nice to make this an instance but it is empirically problematic, possibly because
--- of the loop that it causes with `Module.IsNoetherian.finite`
-theorem isNoetherian_of_isNoetherianRing_of_finite (R M : Type*)
+instance isNoetherian_of_isNoetherianRing_of_finite (R M : Type*)
     [Ring R] [AddCommGroup M] [Module R M] [IsNoetherianRing R] [Module.Finite R M] :
     IsNoetherian R M :=
   have : IsNoetherian R (⊤ : Submodule R M) :=

210657c4

chore: space after ← (#8178)

Co-authored-by: Moritz Firsching <firsching@google.com>

5fb9beab

Diff

@@ -410,7 +410,7 @@ theorem finite_of_linearIndependent [Nontrivial R] {s : Set M}
     exact ⟨fun hab x (hxa : x ≤ a) => le_trans hxa hab, fun hx => hx a (le_refl a)⟩
   exact
     ⟨⟨fun n => span R (coe' ∘ f '' { m | m ≤ n }), fun x y => by
-        rw [le_antisymm_iff, (this x y).symm, (this y x).symm, ←le_antisymm_iff, imp_self]
+        rw [le_antisymm_iff, (this x y).symm, (this y x).symm, ← le_antisymm_iff, imp_self]
         trivial⟩,
       by dsimp [GT.gt]; simp only [lt_iff_le_not_le, (this _ _).symm]; tauto⟩
 #align finite_of_linear_independent finite_of_linearIndependent

210657c4

feat: the trace of a direct sum is the sum of the traces (#8369)

0e1fb8d5

Diff

@@ -386,6 +386,12 @@ universe w
 variable {R M P : Type*} {N : Type w} [Ring R] [AddCommGroup M] [Module R M] [AddCommGroup N]
   [Module R N] [AddCommGroup P] [Module R P] [IsNoetherian R M]
 
+lemma Submodule.finite_ne_bot_of_independent {ι : Type*} {N : ι → Submodule R M}
+    (h : CompleteLattice.Independent N) :
+    Set.Finite {i | N i ≠ ⊥} :=
+  CompleteLattice.WellFounded.finite_ne_bot_of_independent
+    (isNoetherian_iff_wellFounded.mp inferInstance) h
+
 theorem finite_of_linearIndependent [Nontrivial R] {s : Set M}
     (hs : LinearIndependent R ((↑) : s → M)) : s.Finite := by
   refine'

210657c4

feat: improve API for Fitting decomposition of a linear endomorphism (#7487)

Especially the new lemma LinearMap.eventually_isCompl_ker_pow_range_pow

b400da17

Diff

@@ -9,6 +9,7 @@ import Mathlib.Algebra.Ring.Idempotents
 import Mathlib.GroupTheory.Finiteness
 import Mathlib.LinearAlgebra.LinearIndependent
 import Mathlib.Order.CompactlyGenerated
+import Mathlib.Order.Filter.EventuallyConst
 import Mathlib.Order.OrderIsoNat
 import Mathlib.RingTheory.Finiteness
 import Mathlib.RingTheory.Nilpotent
@@ -57,9 +58,7 @@ Noetherian, noetherian, Noetherian ring, Noetherian module, noetherian ring, noe
 -/
 
 
-open Set
-
-open BigOperators Pointwise
+open Set Filter BigOperators Pointwise
 
 /-- `IsNoetherian R M` is the proposition that `M` is a Noetherian `R`-module,
 implemented as the predicate that all `R`-submodules of `M` are finitely generated.
@@ -367,6 +366,11 @@ theorem monotone_stabilizes_iff_noetherian :
   rw [isNoetherian_iff_wellFounded, WellFounded.monotone_chain_condition]
 #align monotone_stabilizes_iff_noetherian monotone_stabilizes_iff_noetherian
 
+theorem eventuallyConst_of_isNoetherian [IsNoetherian R M] (f : ℕ →o Submodule R M) :
+    atTop.EventuallyConst f := by
+  simp_rw [eventuallyConst_atTop, eq_comm]
+  exact (monotone_stabilizes_iff_noetherian.mpr inferInstance) f
+
 /-- If `∀ I > J, P I` implies `P J`, then `P` holds for all submodules. -/
 theorem IsNoetherian.induction [IsNoetherian R M] {P : Submodule R M → Prop}
     (hgt : ∀ I, (∀ J > I, P J) → P I) (I : Submodule R M) : P I :=
@@ -380,9 +384,9 @@ section
 universe w
 
 variable {R M P : Type*} {N : Type w} [Ring R] [AddCommGroup M] [Module R M] [AddCommGroup N]
-  [Module R N] [AddCommGroup P] [Module R P]
+  [Module R N] [AddCommGroup P] [Module R P] [IsNoetherian R M]
 
-theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M}
+theorem finite_of_linearIndependent [Nontrivial R] {s : Set M}
     (hs : LinearIndependent R ((↑) : s → M)) : s.Finite := by
   refine'
     by_contradiction fun hf =>
@@ -407,7 +411,7 @@ theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M
 
 /-- If the first and final modules in a short exact sequence are Noetherian,
   then the middle module is also Noetherian. -/
-theorem isNoetherian_of_range_eq_ker [IsNoetherian R M] [IsNoetherian R P] (f : M →ₗ[R] N)
+theorem isNoetherian_of_range_eq_ker [IsNoetherian R P] (f : M →ₗ[R] N)
     (g : N →ₗ[R] P) (hf : Function.Injective f) (hg : Function.Surjective g)
     (h : LinearMap.range f = LinearMap.ker g) :
     IsNoetherian R N :=
@@ -418,39 +422,43 @@ theorem isNoetherian_of_range_eq_ker [IsNoetherian R M] [IsNoetherian R P] (f :
       (by simp [Submodule.map_comap_eq, inf_comm]) (by simp [Submodule.comap_map_eq, h])
 #align is_noetherian_of_range_eq_ker isNoetherian_of_range_eq_ker
 
-/-- For any endomorphism of a Noetherian module, there is some nontrivial iterate
-with disjoint kernel and range.
--/
-theorem IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot [I : IsNoetherian R M]
-    (f : M →ₗ[R] M) :
-    ∃ n : ℕ, n ≠ 0 ∧ LinearMap.ker (f ^ n) ⊓ LinearMap.range (f ^ n) = ⊥ := by
-  obtain ⟨n, w⟩ :=
-    monotone_stabilizes_iff_noetherian.mpr I
-      (f.iterateKer.comp ⟨fun n => n + 1, fun n m w => by linarith⟩)
-  specialize w (2 * n + 1) (by linarith only)
-  dsimp at w
-  refine' ⟨n + 1, Nat.succ_ne_zero _, _⟩
-  rw [eq_bot_iff]
-  rintro - ⟨h, ⟨y, rfl⟩⟩
-  rw [mem_bot, ← LinearMap.mem_ker, w]
-  erw [LinearMap.mem_ker] at h ⊢
-  change (f ^ (n + 1) * f ^ (n + 1)) y = 0 at h
-  rw [← pow_add] at h
-  convert h using 3
-  ring
-#align is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot
+/-- For an endomorphism of a Noetherian module, any sufficiently large iterate has disjoint kernel
+and range. -/
+theorem LinearMap.eventually_disjoint_ker_pow_range_pow (f : M →ₗ[R] M) :
+    ∀ᶠ n in atTop, Disjoint (LinearMap.ker (f ^ n)) (LinearMap.range (f ^ n)) := by
+  obtain ⟨n, hn : ∀ m, n ≤ m → LinearMap.ker (f ^ n) = LinearMap.ker (f ^ m)⟩ :=
+    monotone_stabilizes_iff_noetherian.mpr inferInstance f.iterateKer
+  refine eventually_atTop.mpr ⟨n, fun m hm ↦ disjoint_iff.mpr ?_⟩
+  rw [← hn _ hm, Submodule.eq_bot_iff]
+  rintro - ⟨hx, ⟨x, rfl⟩⟩
+  apply LinearMap.pow_map_zero_of_le hm
+  replace hx : x ∈ LinearMap.ker (f ^ (n + m)) := by
+    simpa [f.pow_apply n, f.pow_apply m, ← f.pow_apply (n + m), ← iterate_add_apply] using hx
+  rwa [← hn _ (n.le_add_right m)] at hx
+#align is_noetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot LinearMap.eventually_disjoint_ker_pow_range_pow
+
+lemma LinearMap.eventually_iSup_ker_pow_eq (f : M →ₗ[R] M) :
+    ∀ᶠ n in atTop, ⨆ m, LinearMap.ker (f ^ m) = LinearMap.ker (f ^ n) := by
+  obtain ⟨n, hn : ∀ m, n ≤ m → ker (f ^ n) = ker (f ^ m)⟩ :=
+    monotone_stabilizes_iff_noetherian.mpr inferInstance f.iterateKer
+  refine eventually_atTop.mpr ⟨n, fun m hm ↦ ?_⟩
+  refine le_antisymm (iSup_le fun l ↦ ?_) (le_iSup (fun i ↦ LinearMap.ker (f ^ i)) m)
+  cases' le_or_lt m l with h h
+  · rw [← hn _ (hm.trans h), hn _ hm]
+  · exact f.iterateKer.monotone h.le
 
 /-- Any surjective endomorphism of a Noetherian module is injective. -/
-theorem IsNoetherian.injective_of_surjective_endomorphism [IsNoetherian R M] (f : M →ₗ[R] M)
+theorem IsNoetherian.injective_of_surjective_endomorphism (f : M →ₗ[R] M)
     (s : Surjective f) : Injective f := by
-  obtain ⟨n, ne, w⟩ := IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot f
-  rw [LinearMap.range_eq_top.mpr (LinearMap.iterate_surjective s n), inf_top_eq,
-    LinearMap.ker_eq_bot] at w
-  exact LinearMap.injective_of_iterate_injective ne w
+  obtain ⟨n, hn⟩ := eventually_atTop.mp f.eventually_disjoint_ker_pow_range_pow
+  specialize hn (n + 1) (n.le_add_right 1)
+  rw [disjoint_iff, LinearMap.range_eq_top.mpr (LinearMap.iterate_surjective s _), inf_top_eq,
+    LinearMap.ker_eq_bot] at hn
+  exact LinearMap.injective_of_iterate_injective n.succ_ne_zero hn
 #align is_noetherian.injective_of_surjective_endomorphism IsNoetherian.injective_of_surjective_endomorphism
 
 /-- Any surjective endomorphism of a Noetherian module is bijective. -/
-theorem IsNoetherian.bijective_of_surjective_endomorphism [IsNoetherian R M] (f : M →ₗ[R] M)
+theorem IsNoetherian.bijective_of_surjective_endomorphism (f : M →ₗ[R] M)
     (s : Surjective f) : Bijective f :=
   ⟨IsNoetherian.injective_of_surjective_endomorphism f s, s⟩
 #align is_noetherian.bijective_of_surjective_endomorphism IsNoetherian.bijective_of_surjective_endomorphism
@@ -459,7 +467,7 @@ theorem IsNoetherian.bijective_of_surjective_endomorphism [IsNoetherian R M] (f
 with `f (n+1)` disjoint from the supremum of `f 0`, ..., `f n`,
 is eventually zero.
 -/
-theorem IsNoetherian.disjoint_partialSups_eventually_bot [I : IsNoetherian R M]
+theorem IsNoetherian.disjoint_partialSups_eventually_bot
     (f : ℕ → Submodule R M) (h : ∀ n, Disjoint (partialSups f n) (f (n + 1))) :
     ∃ n : ℕ, ∀ m, n ≤ m → f m = ⊥ := by
   -- A little off-by-one cleanup first:
@@ -470,7 +478,7 @@ theorem IsNoetherian.disjoint_partialSups_eventually_bot [I : IsNoetherian R M]
     · cases p
     · apply w
       exact Nat.succ_le_succ_iff.mp p
-  obtain ⟨n, w⟩ := monotone_stabilizes_iff_noetherian.mpr I (partialSups f)
+  obtain ⟨n, w⟩ := monotone_stabilizes_iff_noetherian.mpr inferInstance (partialSups f)
   exact
     ⟨n, fun m p =>
       (h m).eq_bot_of_ge <| sup_eq_left.1 <| (w (m + 1) <| le_add_right p).symm.trans <| w m p⟩
@@ -478,7 +486,7 @@ theorem IsNoetherian.disjoint_partialSups_eventually_bot [I : IsNoetherian R M]
 
 /-- If `M ⊕ N` embeds into `M`, for `M` noetherian over `R`, then `N` is trivial.
 -/
-noncomputable def IsNoetherian.equivPUnitOfProdInjective [IsNoetherian R M] (f : M × N →ₗ[R] M)
+noncomputable def IsNoetherian.equivPUnitOfProdInjective (f : M × N →ₗ[R] M)
     (i : Injective f) : N ≃ₗ[R] PUnit.{w + 1} := by
   apply Nonempty.some
   obtain ⟨n, w⟩ :=

210657c4

feat: Hom(N, M) is Noetherian when M is Noetherian and N is finitely-generated. (#7276)

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

63ca289d

Diff

@@ -286,6 +286,21 @@ instance isNoetherian_pi' {R ι M : Type*} [Ring R] [AddCommGroup M] [Module R M
 
 end
 
+section CommRing
+
+variable (R M N : Type*) [CommRing R] [AddCommGroup M] [AddCommGroup N] [Module R M] [Module R N]
+  [IsNoetherian R M] [Module.Finite R N]
+
+instance isNoetherian_linearMap_pi {ι : Type*} [Finite ι] : IsNoetherian R ((ι → R) →ₗ[R] M) :=
+  let _i : Fintype ι := Fintype.ofFinite ι; isNoetherian_of_linearEquiv (Module.piEquiv ι R M)
+
+instance isNoetherian_linearMap : IsNoetherian R (N →ₗ[R] M) := by
+  obtain ⟨n, f, hf⟩ := Module.Finite.exists_fin' R N
+  let g : (N →ₗ[R] M) →ₗ[R] (Fin n → R) →ₗ[R] M := (LinearMap.llcomp R (Fin n → R) N M).flip f
+  exact isNoetherian_of_injective g hf.injective_linearMapComp_right
+
+end CommRing
+
 open IsNoetherian Submodule Function
 
 section

210657c4

chore: restate isNoetherian_of_fg_of_noetherian' using Module.Finite (and rename). (#6609)

d8130a5e

Diff

@@ -565,11 +565,15 @@ theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module
     rw [Finsupp.not_mem_support_iff.1 hx, zero_smul]
 #align is_noetherian_of_fg_of_noetherian isNoetherian_of_fg_of_noetherian
 
-theorem isNoetherian_of_fg_of_noetherian' {R M} [Ring R] [AddCommGroup M] [Module R M]
-    [IsNoetherianRing R] (h : (⊤ : Submodule R M).FG) : IsNoetherian R M :=
-  have : IsNoetherian R (⊤ : Submodule R M) := isNoetherian_of_fg_of_noetherian _ h
+-- It would be nice to make this an instance but it is empirically problematic, possibly because
+-- of the loop that it causes with `Module.IsNoetherian.finite`
+theorem isNoetherian_of_isNoetherianRing_of_finite (R M : Type*)
+    [Ring R] [AddCommGroup M] [Module R M] [IsNoetherianRing R] [Module.Finite R M] :
+    IsNoetherian R M :=
+  have : IsNoetherian R (⊤ : Submodule R M) :=
+    isNoetherian_of_fg_of_noetherian _ $ Module.finite_def.mp inferInstance
   isNoetherian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl)
-#align is_noetherian_of_fg_of_noetherian' isNoetherian_of_fg_of_noetherian'
+#align is_noetherian_of_fg_of_noetherian' isNoetherian_of_isNoetherianRing_of_finite
 
 /-- In a module over a Noetherian ring, the submodule generated by finitely many vectors is
 Noetherian. -/

210657c4

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -73,7 +73,7 @@ attribute [inherit_doc IsNoetherian] IsNoetherian.noetherian
 
 section
 
-variable {R : Type _} {M : Type _} {P : Type _}
+variable {R : Type*} {M : Type*} {P : Type*}
 
 variable [Semiring R] [AddCommMonoid M] [AddCommMonoid P]
 
@@ -154,7 +154,7 @@ end
 
 namespace Module
 
-variable {R M N : Type _}
+variable {R M N : Type*}
 
 variable [Semiring R] [AddCommMonoid M] [AddCommMonoid N] [Module R M] [Module R N]
 
@@ -176,7 +176,7 @@ end Module
 
 section
 
-variable {R : Type _} {M : Type _} {P : Type _}
+variable {R : Type*} {M : Type*} {P : Type*}
 
 variable [Ring R] [AddCommGroup M] [AddCommGroup P]
 
@@ -203,7 +203,7 @@ instance isNoetherian_prod [IsNoetherian R M] [IsNoetherian R P] : IsNoetherian
       Submodule.map_comap_eq_self this ▸ (noetherian _).map _⟩
 #align is_noetherian_prod isNoetherian_prod
 
-instance isNoetherian_pi {R ι : Type _} {M : ι → Type _}
+instance isNoetherian_pi {R ι : Type*} {M : ι → Type*}
     [Ring R] [∀ i, AddCommGroup (M i)] [∀ i, Module R (M i)] [Finite ι]
     [∀ i, IsNoetherian R (M i)] : IsNoetherian R (∀ i, M i) := by
   cases nonempty_fintype ι
@@ -279,7 +279,7 @@ instance isNoetherian_pi {R ι : Type _} {M : ι → Type _}
 /-- A version of `isNoetherian_pi` for non-dependent functions. We need this instance because
 sometimes Lean fails to apply the dependent version in non-dependent settings (e.g., it fails to
 prove that `ι → ℝ` is finite dimensional over `ℝ`). -/
-instance isNoetherian_pi' {R ι M : Type _} [Ring R] [AddCommGroup M] [Module R M] [Finite ι]
+instance isNoetherian_pi' {R ι M : Type*} [Ring R] [AddCommGroup M] [Module R M] [Finite ι]
     [IsNoetherian R M] : IsNoetherian R (ι → M) :=
   isNoetherian_pi
 #align is_noetherian_pi' isNoetherian_pi'
@@ -292,7 +292,7 @@ section
 
 universe w
 
-variable {R M P : Type _} {N : Type w} [Semiring R] [AddCommMonoid M] [Module R M] [AddCommMonoid N]
+variable {R M P : Type*} {N : Type w} [Semiring R] [AddCommMonoid M] [Module R M] [AddCommMonoid N]
   [Module R N] [AddCommMonoid P] [Module R P]
 
 theorem isNoetherian_iff_wellFounded :
@@ -364,7 +364,7 @@ section
 
 universe w
 
-variable {R M P : Type _} {N : Type w} [Ring R] [AddCommGroup M] [Module R M] [AddCommGroup N]
+variable {R M P : Type*} {N : Type w} [Ring R] [AddCommGroup M] [Module R M] [AddCommGroup N]
   [Module R N] [AddCommGroup P] [Module R P]
 
 theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M}
@@ -491,7 +491,7 @@ theorem isNoetherianRing_iff {R} [Semiring R] : IsNoetherianRing R ↔ IsNoether
 #align is_noetherian_ring_iff isNoetherianRing_iff
 
 /-- A ring is Noetherian if and only if all its ideals are finitely-generated. -/
-theorem isNoetherianRing_iff_ideal_fg (R : Type _) [Semiring R] :
+theorem isNoetherianRing_iff_ideal_fg (R : Type*) [Semiring R] :
     IsNoetherianRing R ↔ ∀ I : Ideal R, I.FG :=
   isNoetherianRing_iff.trans isNoetherian_def
 #align is_noetherian_ring_iff_ideal_fg isNoetherianRing_iff_ideal_fg
@@ -594,7 +594,7 @@ theorem isNoetherianRing_of_ringEquiv (R) [Ring R] {S} [Ring S] (f : R ≃+* S)
   isNoetherianRing_of_surjective R S f.toRingHom f.toEquiv.surjective
 #align is_noetherian_ring_of_ring_equiv isNoetherianRing_of_ringEquiv
 
-theorem IsNoetherianRing.isNilpotent_nilradical (R : Type _) [CommRing R] [IsNoetherianRing R] :
+theorem IsNoetherianRing.isNilpotent_nilradical (R : Type*) [CommRing R] [IsNoetherianRing R] :
     IsNilpotent (nilradical R) := by
   obtain ⟨n, hn⟩ := Ideal.exists_radical_pow_le_of_fg (⊥ : Ideal R) (IsNoetherian.noetherian _)
   exact ⟨n, eq_bot_iff.mpr hn⟩

210657c4

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2018 Mario Carneiro, Kevin Buzzard. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Kevin Buzzard
-
-! This file was ported from Lean 3 source module ring_theory.noetherian
-! leanprover-community/mathlib commit 210657c4ea4a4a7b234392f70a3a2a83346dfa90
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Algebra.Subalgebra.Basic
 import Mathlib.Algebra.Algebra.Tower
@@ -18,6 +13,8 @@ import Mathlib.Order.OrderIsoNat
 import Mathlib.RingTheory.Finiteness
 import Mathlib.RingTheory.Nilpotent
 
+#align_import ring_theory.noetherian from "leanprover-community/mathlib"@"210657c4ea4a4a7b234392f70a3a2a83346dfa90"
+
 /-!
 # Noetherian rings and modules

210657c4

chore: clean up spacing around at and goals (#5387)

Changes are of the form

some_tactic at h⊢ -> some_tactic at h ⊢
some_tactic at h -> some_tactic at h

2a870323

Diff

@@ -421,7 +421,7 @@ theorem IsNoetherian.exists_endomorphism_iterate_ker_inf_range_eq_bot [I : IsNoe
   rw [eq_bot_iff]
   rintro - ⟨h, ⟨y, rfl⟩⟩
   rw [mem_bot, ← LinearMap.mem_ker, w]
-  erw [LinearMap.mem_ker] at h⊢
+  erw [LinearMap.mem_ker] at h ⊢
   change (f ^ (n + 1) * f ^ (n + 1)) y = 0 at h
   rw [← pow_add] at h
   convert h using 3
@@ -515,13 +515,13 @@ instance (priority := 100) isNoetherian_of_subsingleton (R M) [Subsingleton R] [
 
 theorem isNoetherian_of_submodule_of_noetherian (R M) [Semiring R] [AddCommMonoid M] [Module R M]
     (N : Submodule R M) (h : IsNoetherian R M) : IsNoetherian R N := by
-  rw [isNoetherian_iff_wellFounded] at h⊢
+  rw [isNoetherian_iff_wellFounded] at h ⊢
   exact OrderEmbedding.wellFounded (Submodule.MapSubtype.orderEmbedding N).dual h
 #align is_noetherian_of_submodule_of_noetherian isNoetherian_of_submodule_of_noetherian
 
 instance Submodule.Quotient.isNoetherian {R} [Ring R] {M} [AddCommGroup M] [Module R M]
     (N : Submodule R M) [h : IsNoetherian R M] : IsNoetherian R (M ⧸ N) := by
-  rw [isNoetherian_iff_wellFounded] at h⊢
+  rw [isNoetherian_iff_wellFounded] at h ⊢
   exact OrderEmbedding.wellFounded (Submodule.comapMkQOrderEmbedding N).dual h
 #align submodule.quotient.is_noetherian Submodule.Quotient.isNoetherian
 
@@ -529,7 +529,7 @@ instance Submodule.Quotient.isNoetherian {R} [Ring R] {M} [AddCommGroup M] [Modu
 also noetherian. -/
 theorem isNoetherian_of_tower (R) {S M} [Semiring R] [Semiring S] [AddCommMonoid M] [SMul R S]
     [Module S M] [Module R M] [IsScalarTower R S M] (h : IsNoetherian R M) : IsNoetherian S M := by
-  rw [isNoetherian_iff_wellFounded] at h⊢
+  rw [isNoetherian_iff_wellFounded] at h ⊢
   refine' (Submodule.restrictScalarsEmbedding R S M).dual.wellFounded h
 #align is_noetherian_of_tower isNoetherian_of_tower
 
@@ -583,7 +583,7 @@ theorem isNoetherian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R
 
 theorem isNoetherianRing_of_surjective (R) [Ring R] (S) [Ring S] (f : R →+* S)
     (hf : Function.Surjective f) [H : IsNoetherianRing R] : IsNoetherianRing S := by
-  rw [isNoetherianRing_iff, isNoetherian_iff_wellFounded] at H⊢
+  rw [isNoetherianRing_iff, isNoetherian_iff_wellFounded] at H ⊢
   exact OrderEmbedding.wellFounded (Ideal.orderEmbeddingOfSurjective f hf).dual H
 #align is_noetherian_ring_of_surjective isNoetherianRing_of_surjective

210657c4

chore: tidy various files (#4757)

ea80818c

Diff

@@ -466,7 +466,7 @@ theorem IsNoetherian.disjoint_partialSups_eventually_bot [I : IsNoetherian R M]
 
 /-- If `M ⊕ N` embeds into `M`, for `M` noetherian over `R`, then `N` is trivial.
 -/
-noncomputable def IsNoetherian.equivPunitOfProdInjective [IsNoetherian R M] (f : M × N →ₗ[R] M)
+noncomputable def IsNoetherian.equivPUnitOfProdInjective [IsNoetherian R M] (f : M × N →ₗ[R] M)
     (i : Injective f) : N ≃ₗ[R] PUnit.{w + 1} := by
   apply Nonempty.some
   obtain ⟨n, w⟩ :=
@@ -477,7 +477,7 @@ noncomputable def IsNoetherian.equivPunitOfProdInjective [IsNoetherian R M] (f :
   refine (LinearMap.tailingLinearEquiv f i n).symm ≪≫ₗ ?_
   rw [w]
   apply Submodule.botEquivPUnit
-#align is_noetherian.equiv_punit_of_prod_injective IsNoetherian.equivPunitOfProdInjective
+#align is_noetherian.equiv_punit_of_prod_injective IsNoetherian.equivPUnitOfProdInjective
 
 end

210657c4

chore: delete 2074 references (#4030)

1877b122

Diff

@@ -406,10 +406,6 @@ theorem isNoetherian_of_range_eq_ker [IsNoetherian R M] [IsNoetherian R P] (f :
       (by simp [Submodule.map_comap_eq, inf_comm]) (by simp [Submodule.comap_map_eq, h])
 #align is_noetherian_of_range_eq_ker isNoetherian_of_range_eq_ker
 
-/- Porting note (lean4#2074): this seems to cause a diamond with Ring.toSemiring when going to
-NonAssocSemiring -/
-attribute [-instance] Ring.toNonAssocRing
-
 /-- For any endomorphism of a Noetherian module, there is some nontrivial iterate
 with disjoint kernel and range.
 -/

210657c4

chore: reenable eta, bump to nightly 2023-05-16 (#3414)

Now that leanprover/lean4#2210 has been merged, this PR:

removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
removes many but not quite all set_option maxHeartbeats commands
makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

a6e1045f

Diff

@@ -480,7 +480,7 @@ noncomputable def IsNoetherian.equivPunitOfProdInjective [IsNoetherian R M] (f :
   -- Porting note: refine' makes this line time out at elaborator
   refine (LinearMap.tailingLinearEquiv f i n).symm ≪≫ₗ ?_
   rw [w]
-  exact Submodule.botEquivPUnit
+  apply Submodule.botEquivPUnit
 #align is_noetherian.equiv_punit_of_prod_injective IsNoetherian.equivPunitOfProdInjective
 
 end
@@ -537,7 +537,6 @@ theorem isNoetherian_of_tower (R) {S M} [Semiring R] [Semiring S] [AddCommMonoid
   refine' (Submodule.restrictScalarsEmbedding R S M).dual.wellFounded h
 #align is_noetherian_of_tower isNoetherian_of_tower
 
-set_option synthInstance.etaExperiment true in
 theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module R M]
     (N : Submodule R M) [I : IsNoetherianRing R] (hN : N.FG) : IsNoetherian R N := by
   let ⟨s, hs⟩ := hN

210657c4

refactor: rename Fg to FG (#3948)

Please refer to this Zulip thread: https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Naming.20convention/near/357712556

000e226b

Diff

@@ -69,7 +69,7 @@ implemented as the predicate that all `R`-submodules of `M` are finitely generat
 -/
 -- Porting note: should this be renamed to `Noetherian`?
 class IsNoetherian (R M) [Semiring R] [AddCommMonoid M] [Module R M] : Prop where
-  noetherian : ∀ s : Submodule R M, s.Fg
+  noetherian : ∀ s : Submodule R M, s.FG
 #align is_noetherian IsNoetherian
 
 attribute [inherit_doc IsNoetherian] IsNoetherian.noetherian
@@ -85,12 +85,12 @@ variable [Module R M] [Module R P]
 open IsNoetherian
 
 /-- An R-module is Noetherian iff all its submodules are finitely-generated. -/
-theorem isNoetherian_def : IsNoetherian R M ↔ ∀ s : Submodule R M, s.Fg :=
+theorem isNoetherian_def : IsNoetherian R M ↔ ∀ s : Submodule R M, s.FG :=
   ⟨fun h => h.noetherian, IsNoetherian.mk⟩
 #align is_noetherian_def isNoetherian_def
 
 theorem isNoetherian_submodule {N : Submodule R M} :
-    IsNoetherian R N ↔ ∀ s : Submodule R M, s ≤ N → s.Fg := by
+    IsNoetherian R N ↔ ∀ s : Submodule R M, s ≤ N → s.FG := by
   refine ⟨fun ⟨hn⟩ => fun s hs =>
     have : s ≤ LinearMap.range N.subtype := N.range_subtype.symm ▸ hs
     Submodule.map_comap_eq_self this ▸ (hn _).map _,
@@ -103,12 +103,12 @@ theorem isNoetherian_submodule {N : Submodule R M} :
 #align is_noetherian_submodule isNoetherian_submodule
 
 theorem isNoetherian_submodule_left {N : Submodule R M} :
-    IsNoetherian R N ↔ ∀ s : Submodule R M, (N ⊓ s).Fg :=
+    IsNoetherian R N ↔ ∀ s : Submodule R M, (N ⊓ s).FG :=
   isNoetherian_submodule.trans ⟨fun H _ => H _ inf_le_left, fun H _ hs => inf_of_le_right hs ▸ H _⟩
 #align is_noetherian_submodule_left isNoetherian_submodule_left
 
 theorem isNoetherian_submodule_right {N : Submodule R M} :
-    IsNoetherian R N ↔ ∀ s : Submodule R M, (s ⊓ N).Fg :=
+    IsNoetherian R N ↔ ∀ s : Submodule R M, (s ⊓ N).FG :=
   isNoetherian_submodule.trans ⟨fun H _ => H _ inf_le_right, fun H _ hs => inf_of_le_left hs ▸ H _⟩
 #align is_noetherian_submodule_right isNoetherian_submodule_right
 
@@ -148,7 +148,7 @@ theorem isNoetherian_of_injective [IsNoetherian R P] (f : M →ₗ[R] P) (hf : F
 #align is_noetherian_of_injective isNoetherian_of_injective
 
 theorem fg_of_injective [IsNoetherian R P] {N : Submodule R M} (f : M →ₗ[R] P)
-    (hf : Function.Injective f) : N.Fg :=
+    (hf : Function.Injective f) : N.FG :=
   haveI := isNoetherian_of_injective f hf
   IsNoetherian.noetherian N
 #align fg_of_injective fg_of_injective
@@ -193,7 +193,7 @@ theorem isNoetherian_of_ker_bot [IsNoetherian R P] (f : M →ₗ[R] P) (hf : Lin
 #align is_noetherian_of_ker_bot isNoetherian_of_ker_bot
 
 theorem fg_of_ker_bot [IsNoetherian R P] {N : Submodule R M} (f : M →ₗ[R] P)
-    (hf : LinearMap.ker f = ⊥) : N.Fg :=
+    (hf : LinearMap.ker f = ⊥) : N.FG :=
   haveI := isNoetherian_of_ker_bot f hf
   IsNoetherian.noetherian N
 #align fg_of_ker_bot fg_of_ker_bot
@@ -311,8 +311,8 @@ theorem isNoetherian_iff_wellFounded :
 theorem isNoetherian_iff_fg_wellFounded :
     IsNoetherian R M ↔
       WellFounded
-        ((· > ·) : { N : Submodule R M // N.Fg } → { N : Submodule R M // N.Fg } → Prop) := by
-  let α := { N : Submodule R M // N.Fg }
+        ((· > ·) : { N : Submodule R M // N.FG } → { N : Submodule R M // N.FG } → Prop) := by
+  let α := { N : Submodule R M // N.FG }
   constructor
   · intro H
     let f : α ↪o Submodule R M := OrderEmbedding.subtype _
@@ -328,7 +328,7 @@ theorem isNoetherian_iff_fg_wellFounded :
     obtain ⟨x, hx₁ : x ∈ N, hx₂ : x ∉ N₀⟩ := Set.not_subset.mp h₃
     apply hx₂
     rw [eq_of_le_of_not_lt (le_sup_right : N₀ ≤ _) (h₂
-      ⟨_, Submodule.Fg.sup ⟨{x}, by rw [Finset.coe_singleton]⟩ h₁⟩ <|
+      ⟨_, Submodule.FG.sup ⟨{x}, by rw [Finset.coe_singleton]⟩ h₁⟩ <|
       sup_le ((Submodule.span_singleton_le_iff_mem _ _).mpr hx₁) e)]
     exact (le_sup_left : (R ∙ x) ≤ _) (Submodule.mem_span_singleton_self _)
 #align is_noetherian_iff_fg_well_founded isNoetherian_iff_fg_wellFounded
@@ -499,7 +499,7 @@ theorem isNoetherianRing_iff {R} [Semiring R] : IsNoetherianRing R ↔ IsNoether
 
 /-- A ring is Noetherian if and only if all its ideals are finitely-generated. -/
 theorem isNoetherianRing_iff_ideal_fg (R : Type _) [Semiring R] :
-    IsNoetherianRing R ↔ ∀ I : Ideal R, I.Fg :=
+    IsNoetherianRing R ↔ ∀ I : Ideal R, I.FG :=
   isNoetherianRing_iff.trans isNoetherian_def
 #align is_noetherian_ring_iff_ideal_fg isNoetherianRing_iff_ideal_fg
 
@@ -539,7 +539,7 @@ theorem isNoetherian_of_tower (R) {S M} [Semiring R] [Semiring S] [AddCommMonoid
 
 set_option synthInstance.etaExperiment true in
 theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module R M]
-    (N : Submodule R M) [I : IsNoetherianRing R] (hN : N.Fg) : IsNoetherian R N := by
+    (N : Submodule R M) [I : IsNoetherianRing R] (hN : N.FG) : IsNoetherian R N := by
   let ⟨s, hs⟩ := hN
   haveI := Classical.decEq M
   haveI := Classical.decEq R
@@ -574,7 +574,7 @@ theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module
 #align is_noetherian_of_fg_of_noetherian isNoetherian_of_fg_of_noetherian
 
 theorem isNoetherian_of_fg_of_noetherian' {R M} [Ring R] [AddCommGroup M] [Module R M]
-    [IsNoetherianRing R] (h : (⊤ : Submodule R M).Fg) : IsNoetherian R M :=
+    [IsNoetherianRing R] (h : (⊤ : Submodule R M).FG) : IsNoetherian R M :=
   have : IsNoetherian R (⊤ : Submodule R M) := isNoetherian_of_fg_of_noetherian _ h
   isNoetherian_of_linearEquiv (LinearEquiv.ofTop (⊤ : Submodule R M) rfl)
 #align is_noetherian_of_fg_of_noetherian' isNoetherian_of_fg_of_noetherian'

210657c4

chore(*): tweak priorities for linear algebra (#3840)

We make sure that the canonical path from NonAssocSemiring to Ring passes through Semiring, as this is a path which is followed all the time in linear algebra where the defining semilinear map σ : R →+* S depends on the NonAssocSemiring structure of R and S while the module definition depends on the Semiring structure.

Tt is not currently possible to adjust priorities by hand (see lean4#2115). Instead, the last declared instance is used, so we make sure that Semiring is declared after NonAssocRing, so that Semiring -> NonAssocSemiring is tried before NonAssocRing -> NonAssocSemiring.

0d22228a

Diff

@@ -187,13 +187,11 @@ variable [Module R M] [Module R P]
 
 open IsNoetherian
 
-set_option synthInstance.etaExperiment true in
 theorem isNoetherian_of_ker_bot [IsNoetherian R P] (f : M →ₗ[R] P) (hf : LinearMap.ker f = ⊥) :
     IsNoetherian R M :=
   isNoetherian_of_linearEquiv (LinearEquiv.ofInjective f <| LinearMap.ker_eq_bot.mp hf).symm
 #align is_noetherian_of_ker_bot isNoetherian_of_ker_bot
 
-set_option synthInstance.etaExperiment true in
 theorem fg_of_ker_bot [IsNoetherian R P] {N : Submodule R M} (f : M →ₗ[R] P)
     (hf : LinearMap.ker f = ⊥) : N.Fg :=
   haveI := isNoetherian_of_ker_bot f hf
@@ -395,7 +393,6 @@ theorem finite_of_linearIndependent [Nontrivial R] [IsNoetherian R M] {s : Set M
       by dsimp [GT.gt]; simp only [lt_iff_le_not_le, (this _ _).symm]; tauto⟩
 #align finite_of_linear_independent finite_of_linearIndependent
 
-set_option synthInstance.etaExperiment true in
 /-- If the first and final modules in a short exact sequence are Noetherian,
   then the middle module is also Noetherian. -/
 theorem isNoetherian_of_range_eq_ker [IsNoetherian R M] [IsNoetherian R P] (f : M →ₗ[R] N)
@@ -589,7 +586,6 @@ theorem isNoetherian_span_of_finite (R) {M} [Ring R] [AddCommGroup M] [Module R
   isNoetherian_of_fg_of_noetherian _ (Submodule.fg_def.mpr ⟨A, hA, rfl⟩)
 #align is_noetherian_span_of_finite isNoetherian_span_of_finite
 
-set_option synthInstance.etaExperiment true in
 theorem isNoetherianRing_of_surjective (R) [Ring R] (S) [Ring S] (f : R →+* S)
     (hf : Function.Surjective f) [H : IsNoetherianRing R] : IsNoetherianRing S := by
   rw [isNoetherianRing_iff, isNoetherian_iff_wellFounded] at H⊢

210657c4

chore: use etaExperiment rather than hacking with instances (#3668)

This is to fix timeouts in https://github.com/leanprover-community/mathlib4/pull/3552.

See discussion at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/!4.233552.20.28LinearAlgebra.2EMatrix.2EToLin.29.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

0f225a7f

Diff

@@ -540,13 +540,12 @@ theorem isNoetherian_of_tower (R) {S M} [Semiring R] [Semiring S] [AddCommMonoid
   refine' (Submodule.restrictScalarsEmbedding R S M).dual.wellFounded h
 #align is_noetherian_of_tower isNoetherian_of_tower
 
+set_option synthInstance.etaExperiment true in
 theorem isNoetherian_of_fg_of_noetherian {R M} [Ring R] [AddCommGroup M] [Module R M]
     (N : Submodule R M) [I : IsNoetherianRing R] (hN : N.Fg) : IsNoetherian R N := by
   let ⟨s, hs⟩ := hN
   haveI := Classical.decEq M
   haveI := Classical.decEq R
-  -- Porting note: etaExperiment fixes inferInstance proof
-  letI : IsNoetherian R R := I
   have : ∀ x ∈ s, x ∈ N := fun x hx => hs ▸ Submodule.subset_span hx
   refine
     @isNoetherian_of_surjective

210657c4

feat: port #15071 (#3248)

Mathlib 3: https://github.com/leanprover-community/mathlib/pull/15071

3d1eb786

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Kevin Buzzard
 
 ! This file was ported from Lean 3 source module ring_theory.noetherian
-! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
+! leanprover-community/mathlib commit 210657c4ea4a4a7b234392f70a3a2a83346dfa90
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -323,21 +323,16 @@ theorem isNoetherian_iff_fg_wellFounded :
     constructor
     intro N
     obtain ⟨⟨N₀, h₁⟩, e : N₀ ≤ N, h₂⟩ :=
-      WellFounded.wellFounded_iff_has_max'.mp H { N' : α | N'.1 ≤ N }
-        ⟨⟨⊥, Submodule.fg_bot⟩, @bot_le _ _ _ N⟩
+      WellFounded.has_min H { N' : α | N'.1 ≤ N } ⟨⟨⊥, Submodule.fg_bot⟩, @bot_le _ _ _ N⟩
     convert h₁
     refine' (e.antisymm _).symm
     by_contra h₃
     obtain ⟨x, hx₁ : x ∈ N, hx₂ : x ∉ N₀⟩ := Set.not_subset.mp h₃
     apply hx₂
-    have := h₂ ⟨(R ∙ x) ⊔ N₀, ?_⟩ ?_ ?_
-    · injection this with eq
-      rw [← eq]
-      exact (le_sup_left : (R ∙ x) ≤ (R ∙ x) ⊔ N₀) (Submodule.mem_span_singleton_self _)
-    · exact Submodule.Fg.sup ⟨{x}, by rw [Finset.coe_singleton]⟩ h₁
-    · exact sup_le ((Submodule.span_singleton_le_iff_mem _ _).mpr hx₁) e
-    · show N₀ ≤ (R ∙ x) ⊔ N₀
-      exact le_sup_right
+    rw [eq_of_le_of_not_lt (le_sup_right : N₀ ≤ _) (h₂
+      ⟨_, Submodule.Fg.sup ⟨{x}, by rw [Finset.coe_singleton]⟩ h₁⟩ <|
+      sup_le ((Submodule.span_singleton_le_iff_mem _ _).mpr hx₁) e)]
+    exact (le_sup_left : (R ∙ x) ≤ _) (Submodule.mem_span_singleton_self _)
 #align is_noetherian_iff_fg_well_founded isNoetherian_iff_fg_wellFounded
 
 variable (R M)
@@ -352,9 +347,8 @@ variable {R M}
 /-- A module is Noetherian iff every nonempty set of submodules has a maximal submodule among them.
 -/
 theorem set_has_maximal_iff_noetherian :
-    (∀ a : Set <| Submodule R M, a.Nonempty → ∃ M' ∈ a, ∀ I ∈ a, M' ≤ I → I = M') ↔
-      IsNoetherian R M :=
-  by rw [isNoetherian_iff_wellFounded, WellFounded.wellFounded_iff_has_max']
+    (∀ a : Set <| Submodule R M, a.Nonempty → ∃ M' ∈ a, ∀ I ∈ a, ¬M' < I) ↔ IsNoetherian R M := by
+  rw [isNoetherian_iff_wellFounded, WellFounded.wellFounded_iff_has_min]
 #align set_has_maximal_iff_noetherian set_has_maximal_iff_noetherian
 
 /-- A module is Noetherian iff every increasing chain of submodules stabilizes. -/

da420a8c

feat: port RingTheory.Noetherian (#2976)

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

f411c38b

`ring_theory.noetherian` ⟷ `Mathlib.RingTheory.Noetherian`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 462

ring_theory.noetherian ⟷ Mathlib.RingTheory.Noetherian

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 462

`ring_theory.noetherian` ⟷ `Mathlib.RingTheory.Noetherian`